{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A single iteration of gradient method is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\mathbf x_{k+1} = \\mathbf x_{k} - \\alpha_k \\nabla f(\\mathbf x_{k}).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, we consider the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = x[1]^2 + 2x[2]^4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The gradient for this function can be easily determined. We will later consider situations in which the gradient is neither supplied nor easily determined analytically. But right now we assume that it is available and can be entered into Julia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "g (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(x) = [2x[1], 8x[2]^3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we proceed with algorithms, we will plot the function (in fact, its contures) to get some idea how it behaves. For realistically large problems with a few dozens or hundreds variable (or even much higher) this will not be possible but why not using it while we are learning. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Plots.PyPlotBackend()"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots, LaTeXStrings\n",
    "pyplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1_data = x2_data = -5:0.01:5;\n",
    "z_data = [f([x1,x2]) for x2=x2_data, x1=x1_data];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "contour(x1_data,x2_data,z_data,levels=100, xlabel=L\"$x_1$\", ylabel=L\"$x_2$\", xlims=(-5,5), ylims=(-5,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even by a visual inspection it appears that the minimum must be at (0,0). Well, this could have been guessed directly from the function prescription (nonnegative, vanishing only at the origin of the plane)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient method with a constant step length"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we consider a constant length of the step in the descent direction, that is, $\\alpha_k = \\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, LinearAlgebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gradient_method_constant (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gradient_method_constant(f,g,x0,α,ϵ,N)\n",
    "    x = x0\n",
    "    iter = 0\n",
    "    while (norm(g(x)) > ϵ) && iter <= (N-1)\n",
    "        iter = iter+1\n",
    "        x = x - α*g(x)\n",
    "        @printf(\"iter = %3d ||∇f(.)|| = %6.4f f(.) = %2.6f \\n\",iter,norm(g(x)),f(x))\n",
    "    end\n",
    "    return f(x),x\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to set the initial guess of the solution. Sometimes we might have some guidance coming from the application domain, other times this is just a blind guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 2.0\n",
       " 1.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = [2.0, 1.0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose the step length as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we also set the conditions for the algorithm to finish. We set both the numerical tolerance on the norm of the gradient and the maximum number of steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.001"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ϵ = 1e-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter =   1 ||∇f(.)|| = 7.3602 f(.) = 5.274386 \n",
      "iter =   2 ||∇f(.)|| = 6.3434 f(.) = 4.771857 \n",
      "iter =   3 ||∇f(.)|| = 5.6463 f(.) = 4.392574 \n",
      "iter =   4 ||∇f(.)|| = 5.1434 f(.) = 4.088554 \n",
      "iter =   5 ||∇f(.)|| = 4.7648 f(.) = 3.834113 \n",
      "iter =   6 ||∇f(.)|| = 4.4693 f(.) = 3.614357 \n",
      "iter =   7 ||∇f(.)|| = 4.2310 f(.) = 3.420096 \n",
      "iter =   8 ||∇f(.)|| = 4.0336 f(.) = 3.245368 \n",
      "iter =   9 ||∇f(.)|| = 3.8658 f(.) = 3.086132 \n",
      "iter =  10 ||∇f(.)|| = 3.7203 f(.) = 2.939554 \n",
      "iter =  11 ||∇f(.)|| = 3.5918 f(.) = 2.803577 \n",
      "iter =  12 ||∇f(.)|| = 3.4764 f(.) = 2.676671 \n",
      "iter =  13 ||∇f(.)|| = 3.3715 f(.) = 2.557662 \n",
      "iter =  14 ||∇f(.)|| = 3.2751 f(.) = 2.445633 \n",
      "iter =  15 ||∇f(.)|| = 3.1855 f(.) = 2.339852 \n",
      "iter =  16 ||∇f(.)|| = 3.1018 f(.) = 2.239719 \n",
      "iter =  17 ||∇f(.)|| = 3.0229 f(.) = 2.144741 \n",
      "iter =  18 ||∇f(.)|| = 2.9481 f(.) = 2.054500 \n",
      "iter =  19 ||∇f(.)|| = 2.8770 f(.) = 1.968639 \n",
      "iter =  20 ||∇f(.)|| = 2.8090 f(.) = 1.886850 \n",
      "iter =  21 ||∇f(.)|| = 2.7439 f(.) = 1.808862 \n",
      "iter =  22 ||∇f(.)|| = 2.6812 f(.) = 1.734436 \n",
      "iter =  23 ||∇f(.)|| = 2.6208 f(.) = 1.663358 \n",
      "iter =  24 ||∇f(.)|| = 2.5625 f(.) = 1.595437 \n",
      "iter =  25 ||∇f(.)|| = 2.5061 f(.) = 1.530496 \n",
      "iter =  26 ||∇f(.)|| = 2.4514 f(.) = 1.468377 \n",
      "iter =  27 ||∇f(.)|| = 2.3984 f(.) = 1.408933 \n",
      "iter =  28 ||∇f(.)|| = 2.3469 f(.) = 1.352029 \n",
      "iter =  29 ||∇f(.)|| = 2.2968 f(.) = 1.297539 \n",
      "iter =  30 ||∇f(.)|| = 2.2481 f(.) = 1.245346 \n",
      "iter =  31 ||∇f(.)|| = 2.2006 f(.) = 1.195343 \n",
      "iter =  32 ||∇f(.)|| = 2.1544 f(.) = 1.147425 \n",
      "iter =  33 ||∇f(.)|| = 2.1093 f(.) = 1.101498 \n",
      "iter =  34 ||∇f(.)|| = 2.0653 f(.) = 1.057472 \n",
      "iter =  35 ||∇f(.)|| = 2.0224 f(.) = 1.015260 \n",
      "iter =  36 ||∇f(.)|| = 1.9805 f(.) = 0.974783 \n",
      "iter =  37 ||∇f(.)|| = 1.9396 f(.) = 0.935964 \n",
      "iter =  38 ||∇f(.)|| = 1.8996 f(.) = 0.898731 \n",
      "iter =  39 ||∇f(.)|| = 1.8606 f(.) = 0.863016 \n",
      "iter =  40 ||∇f(.)|| = 1.8224 f(.) = 0.828753 \n",
      "iter =  41 ||∇f(.)|| = 1.7851 f(.) = 0.795881 \n",
      "iter =  42 ||∇f(.)|| = 1.7486 f(.) = 0.764340 \n",
      "iter =  43 ||∇f(.)|| = 1.7130 f(.) = 0.734075 \n",
      "iter =  44 ||∇f(.)|| = 1.6781 f(.) = 0.705032 \n",
      "iter =  45 ||∇f(.)|| = 1.6439 f(.) = 0.677159 \n",
      "iter =  46 ||∇f(.)|| = 1.6105 f(.) = 0.650409 \n",
      "iter =  47 ||∇f(.)|| = 1.5779 f(.) = 0.624733 \n",
      "iter =  48 ||∇f(.)|| = 1.5459 f(.) = 0.600089 \n",
      "iter =  49 ||∇f(.)|| = 1.5146 f(.) = 0.576434 \n",
      "iter =  50 ||∇f(.)|| = 1.4840 f(.) = 0.553726 \n",
      "iter =  51 ||∇f(.)|| = 1.4540 f(.) = 0.531927 \n",
      "iter =  52 ||∇f(.)|| = 1.4246 f(.) = 0.511001 \n",
      "iter =  53 ||∇f(.)|| = 1.3959 f(.) = 0.490910 \n",
      "iter =  54 ||∇f(.)|| = 1.3677 f(.) = 0.471621 \n",
      "iter =  55 ||∇f(.)|| = 1.3402 f(.) = 0.453102 \n",
      "iter =  56 ||∇f(.)|| = 1.3132 f(.) = 0.435322 \n",
      "iter =  57 ||∇f(.)|| = 1.2868 f(.) = 0.418249 \n",
      "iter =  58 ||∇f(.)|| = 1.2610 f(.) = 0.401857 \n",
      "iter =  59 ||∇f(.)|| = 1.2356 f(.) = 0.386116 \n",
      "iter =  60 ||∇f(.)|| = 1.2108 f(.) = 0.371002 \n",
      "iter =  61 ||∇f(.)|| = 1.1865 f(.) = 0.356488 \n",
      "iter =  62 ||∇f(.)|| = 1.1627 f(.) = 0.342550 \n",
      "iter =  63 ||∇f(.)|| = 1.1394 f(.) = 0.329166 \n",
      "iter =  64 ||∇f(.)|| = 1.1166 f(.) = 0.316313 \n",
      "iter =  65 ||∇f(.)|| = 1.0943 f(.) = 0.303970 \n",
      "iter =  66 ||∇f(.)|| = 1.0724 f(.) = 0.292116 \n",
      "iter =  67 ||∇f(.)|| = 1.0509 f(.) = 0.280731 \n",
      "iter =  68 ||∇f(.)|| = 1.0299 f(.) = 0.269797 \n",
      "iter =  69 ||∇f(.)|| = 1.0093 f(.) = 0.259297 \n",
      "iter =  70 ||∇f(.)|| = 0.9891 f(.) = 0.249211 \n",
      "iter =  71 ||∇f(.)|| = 0.9694 f(.) = 0.239525 \n",
      "iter =  72 ||∇f(.)|| = 0.9500 f(.) = 0.230221 \n",
      "iter =  73 ||∇f(.)|| = 0.9311 f(.) = 0.221285 \n",
      "iter =  74 ||∇f(.)|| = 0.9125 f(.) = 0.212702 \n",
      "iter =  75 ||∇f(.)|| = 0.8943 f(.) = 0.204459 \n",
      "iter =  76 ||∇f(.)|| = 0.8765 f(.) = 0.196540 \n",
      "iter =  77 ||∇f(.)|| = 0.8590 f(.) = 0.188934 \n",
      "iter =  78 ||∇f(.)|| = 0.8419 f(.) = 0.181628 \n",
      "iter =  79 ||∇f(.)|| = 0.8252 f(.) = 0.174610 \n",
      "iter =  80 ||∇f(.)|| = 0.8088 f(.) = 0.167868 \n",
      "iter =  81 ||∇f(.)|| = 0.7927 f(.) = 0.161393 \n",
      "iter =  82 ||∇f(.)|| = 0.7769 f(.) = 0.155172 \n",
      "iter =  83 ||∇f(.)|| = 0.7615 f(.) = 0.149196 \n",
      "iter =  84 ||∇f(.)|| = 0.7463 f(.) = 0.143455 \n",
      "iter =  85 ||∇f(.)|| = 0.7315 f(.) = 0.137940 \n",
      "iter =  86 ||∇f(.)|| = 0.7170 f(.) = 0.132643 \n",
      "iter =  87 ||∇f(.)|| = 0.7028 f(.) = 0.127553 \n",
      "iter =  88 ||∇f(.)|| = 0.6888 f(.) = 0.122663 \n",
      "iter =  89 ||∇f(.)|| = 0.6751 f(.) = 0.117966 \n",
      "iter =  90 ||∇f(.)|| = 0.6618 f(.) = 0.113453 \n",
      "iter =  91 ||∇f(.)|| = 0.6486 f(.) = 0.109117 \n",
      "iter =  92 ||∇f(.)|| = 0.6358 f(.) = 0.104951 \n",
      "iter =  93 ||∇f(.)|| = 0.6232 f(.) = 0.100949 \n",
      "iter =  94 ||∇f(.)|| = 0.6109 f(.) = 0.097103 \n",
      "iter =  95 ||∇f(.)|| = 0.5988 f(.) = 0.093408 \n",
      "iter =  96 ||∇f(.)|| = 0.5869 f(.) = 0.089859 \n",
      "iter =  97 ||∇f(.)|| = 0.5753 f(.) = 0.086448 \n",
      "iter =  98 ||∇f(.)|| = 0.5640 f(.) = 0.083170 \n",
      "iter =  99 ||∇f(.)|| = 0.5528 f(.) = 0.080021 \n",
      "iter = 100 ||∇f(.)|| = 0.5419 f(.) = 0.076995 \n",
      "iter = 101 ||∇f(.)|| = 0.5312 f(.) = 0.074088 \n",
      "iter = 102 ||∇f(.)|| = 0.5207 f(.) = 0.071294 \n",
      "iter = 103 ||∇f(.)|| = 0.5105 f(.) = 0.068609 \n",
      "iter = 104 ||∇f(.)|| = 0.5004 f(.) = 0.066029 \n",
      "iter = 105 ||∇f(.)|| = 0.4905 f(.) = 0.063550 \n",
      "iter = 106 ||∇f(.)|| = 0.4809 f(.) = 0.061167 \n",
      "iter = 107 ||∇f(.)|| = 0.4714 f(.) = 0.058877 \n",
      "iter = 108 ||∇f(.)|| = 0.4621 f(.) = 0.056677 \n",
      "iter = 109 ||∇f(.)|| = 0.4530 f(.) = 0.054562 \n",
      "iter = 110 ||∇f(.)|| = 0.4441 f(.) = 0.052530 \n",
      "iter = 111 ||∇f(.)|| = 0.4354 f(.) = 0.050577 \n",
      "iter = 112 ||∇f(.)|| = 0.4269 f(.) = 0.048700 \n",
      "iter = 113 ||∇f(.)|| = 0.4185 f(.) = 0.046896 \n",
      "iter = 114 ||∇f(.)|| = 0.4103 f(.) = 0.045161 \n",
      "iter = 115 ||∇f(.)|| = 0.4022 f(.) = 0.043495 \n",
      "iter = 116 ||∇f(.)|| = 0.3944 f(.) = 0.041893 \n",
      "iter = 117 ||∇f(.)|| = 0.3866 f(.) = 0.040353 \n",
      "iter = 118 ||∇f(.)|| = 0.3791 f(.) = 0.038873 \n",
      "iter = 119 ||∇f(.)|| = 0.3716 f(.) = 0.037450 \n",
      "iter = 120 ||∇f(.)|| = 0.3644 f(.) = 0.036082 \n",
      "iter = 121 ||∇f(.)|| = 0.3573 f(.) = 0.034767 \n",
      "iter = 122 ||∇f(.)|| = 0.3503 f(.) = 0.033503 \n",
      "iter = 123 ||∇f(.)|| = 0.3435 f(.) = 0.032288 \n",
      "iter = 124 ||∇f(.)|| = 0.3368 f(.) = 0.031120 \n",
      "iter = 125 ||∇f(.)|| = 0.3302 f(.) = 0.029997 \n",
      "iter = 126 ||∇f(.)|| = 0.3238 f(.) = 0.028917 \n",
      "iter = 127 ||∇f(.)|| = 0.3175 f(.) = 0.027879 \n",
      "iter = 128 ||∇f(.)|| = 0.3113 f(.) = 0.026881 \n",
      "iter = 129 ||∇f(.)|| = 0.3053 f(.) = 0.025921 \n",
      "iter = 130 ||∇f(.)|| = 0.2993 f(.) = 0.024999 \n",
      "iter = 131 ||∇f(.)|| = 0.2935 f(.) = 0.024111 \n",
      "iter = 132 ||∇f(.)|| = 0.2878 f(.) = 0.023258 \n",
      "iter = 133 ||∇f(.)|| = 0.2823 f(.) = 0.022438 \n",
      "iter = 134 ||∇f(.)|| = 0.2768 f(.) = 0.021649 \n",
      "iter = 135 ||∇f(.)|| = 0.2715 f(.) = 0.020890 \n",
      "iter = 136 ||∇f(.)|| = 0.2662 f(.) = 0.020160 \n",
      "iter = 137 ||∇f(.)|| = 0.2611 f(.) = 0.019458 \n",
      "iter = 138 ||∇f(.)|| = 0.2560 f(.) = 0.018783 \n",
      "iter = 139 ||∇f(.)|| = 0.2511 f(.) = 0.018134 \n",
      "iter = 140 ||∇f(.)|| = 0.2463 f(.) = 0.017509 \n",
      "iter = 141 ||∇f(.)|| = 0.2416 f(.) = 0.016909 \n",
      "iter = 142 ||∇f(.)|| = 0.2369 f(.) = 0.016331 \n",
      "iter = 143 ||∇f(.)|| = 0.2324 f(.) = 0.015775 \n",
      "iter = 144 ||∇f(.)|| = 0.2279 f(.) = 0.015240 \n",
      "iter = 145 ||∇f(.)|| = 0.2236 f(.) = 0.014726 \n",
      "iter = 146 ||∇f(.)|| = 0.2193 f(.) = 0.014231 \n",
      "iter = 147 ||∇f(.)|| = 0.2151 f(.) = 0.013754 \n",
      "iter = 148 ||∇f(.)|| = 0.2110 f(.) = 0.013296 \n",
      "iter = 149 ||∇f(.)|| = 0.2070 f(.) = 0.012855 \n",
      "iter = 150 ||∇f(.)|| = 0.2030 f(.) = 0.012431 \n",
      "iter = 151 ||∇f(.)|| = 0.1992 f(.) = 0.012022 \n",
      "iter = 152 ||∇f(.)|| = 0.1954 f(.) = 0.011630 \n",
      "iter = 153 ||∇f(.)|| = 0.1917 f(.) = 0.011251 \n",
      "iter = 154 ||∇f(.)|| = 0.1881 f(.) = 0.010887 \n",
      "iter = 155 ||∇f(.)|| = 0.1845 f(.) = 0.010537 \n",
      "iter = 156 ||∇f(.)|| = 0.1811 f(.) = 0.010200 \n",
      "iter = 157 ||∇f(.)|| = 0.1776 f(.) = 0.009875 \n",
      "iter = 158 ||∇f(.)|| = 0.1743 f(.) = 0.009562 \n",
      "iter = 159 ||∇f(.)|| = 0.1710 f(.) = 0.009261 \n",
      "iter = 160 ||∇f(.)|| = 0.1678 f(.) = 0.008971 \n",
      "iter = 161 ||∇f(.)|| = 0.1647 f(.) = 0.008692 \n",
      "iter = 162 ||∇f(.)|| = 0.1616 f(.) = 0.008424 \n",
      "iter = 163 ||∇f(.)|| = 0.1586 f(.) = 0.008165 \n",
      "iter = 164 ||∇f(.)|| = 0.1556 f(.) = 0.007916 \n",
      "iter = 165 ||∇f(.)|| = 0.1528 f(.) = 0.007676 \n",
      "iter = 166 ||∇f(.)|| = 0.1499 f(.) = 0.007445 \n",
      "iter = 167 ||∇f(.)|| = 0.1471 f(.) = 0.007222 \n",
      "iter = 168 ||∇f(.)|| = 0.1444 f(.) = 0.007007 \n",
      "iter = 169 ||∇f(.)|| = 0.1418 f(.) = 0.006801 \n",
      "iter = 170 ||∇f(.)|| = 0.1392 f(.) = 0.006602 \n",
      "iter = 171 ||∇f(.)|| = 0.1366 f(.) = 0.006410 \n",
      "iter = 172 ||∇f(.)|| = 0.1341 f(.) = 0.006225 \n",
      "iter = 173 ||∇f(.)|| = 0.1317 f(.) = 0.006047 \n",
      "iter = 174 ||∇f(.)|| = 0.1293 f(.) = 0.005875 \n",
      "iter = 175 ||∇f(.)|| = 0.1269 f(.) = 0.005709 \n",
      "iter = 176 ||∇f(.)|| = 0.1246 f(.) = 0.005550 \n",
      "iter = 177 ||∇f(.)|| = 0.1224 f(.) = 0.005396 \n",
      "iter = 178 ||∇f(.)|| = 0.1201 f(.) = 0.005248 \n",
      "iter = 179 ||∇f(.)|| = 0.1180 f(.) = 0.005104 \n",
      "iter = 180 ||∇f(.)|| = 0.1159 f(.) = 0.004967 \n",
      "iter = 181 ||∇f(.)|| = 0.1138 f(.) = 0.004833 \n",
      "iter = 182 ||∇f(.)|| = 0.1118 f(.) = 0.004705 \n",
      "iter = 183 ||∇f(.)|| = 0.1098 f(.) = 0.004581 \n",
      "iter = 184 ||∇f(.)|| = 0.1078 f(.) = 0.004462 \n",
      "iter = 185 ||∇f(.)|| = 0.1059 f(.) = 0.004347 \n",
      "iter = 186 ||∇f(.)|| = 0.1040 f(.) = 0.004236 \n",
      "iter = 187 ||∇f(.)|| = 0.1022 f(.) = 0.004128 \n",
      "iter = 188 ||∇f(.)|| = 0.1004 f(.) = 0.004025 \n",
      "iter = 189 ||∇f(.)|| = 0.0987 f(.) = 0.003925 \n",
      "iter = 190 ||∇f(.)|| = 0.0970 f(.) = 0.003828 \n",
      "iter = 191 ||∇f(.)|| = 0.0953 f(.) = 0.003735 \n",
      "iter = 192 ||∇f(.)|| = 0.0936 f(.) = 0.003645 \n",
      "iter = 193 ||∇f(.)|| = 0.0920 f(.) = 0.003558 \n",
      "iter = 194 ||∇f(.)|| = 0.0904 f(.) = 0.003474 \n",
      "iter = 195 ||∇f(.)|| = 0.0889 f(.) = 0.003393 \n",
      "iter = 196 ||∇f(.)|| = 0.0874 f(.) = 0.003315 \n",
      "iter = 197 ||∇f(.)|| = 0.0859 f(.) = 0.003239 \n",
      "iter = 198 ||∇f(.)|| = 0.0844 f(.) = 0.003166 \n",
      "iter = 199 ||∇f(.)|| = 0.0830 f(.) = 0.003095 \n",
      "iter = 200 ||∇f(.)|| = 0.0816 f(.) = 0.003027 \n",
      "iter = 201 ||∇f(.)|| = 0.0803 f(.) = 0.002961 \n",
      "iter = 202 ||∇f(.)|| = 0.0789 f(.) = 0.002897 \n",
      "iter = 203 ||∇f(.)|| = 0.0776 f(.) = 0.002835 \n",
      "iter = 204 ||∇f(.)|| = 0.0763 f(.) = 0.002775 \n",
      "iter = 205 ||∇f(.)|| = 0.0751 f(.) = 0.002718 \n",
      "iter = 206 ||∇f(.)|| = 0.0739 f(.) = 0.002662 \n",
      "iter = 207 ||∇f(.)|| = 0.0727 f(.) = 0.002608 \n",
      "iter = 208 ||∇f(.)|| = 0.0715 f(.) = 0.002555 \n",
      "iter = 209 ||∇f(.)|| = 0.0704 f(.) = 0.002505 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 210 ||∇f(.)|| = 0.0692 f(.) = 0.002455 \n",
      "iter = 211 ||∇f(.)|| = 0.0681 f(.) = 0.002408 \n",
      "iter = 212 ||∇f(.)|| = 0.0671 f(.) = 0.002362 \n",
      "iter = 213 ||∇f(.)|| = 0.0660 f(.) = 0.002317 \n",
      "iter = 214 ||∇f(.)|| = 0.0650 f(.) = 0.002274 \n",
      "iter = 215 ||∇f(.)|| = 0.0640 f(.) = 0.002232 \n",
      "iter = 216 ||∇f(.)|| = 0.0630 f(.) = 0.002192 \n",
      "iter = 217 ||∇f(.)|| = 0.0620 f(.) = 0.002152 \n",
      "iter = 218 ||∇f(.)|| = 0.0611 f(.) = 0.002114 \n",
      "iter = 219 ||∇f(.)|| = 0.0601 f(.) = 0.002077 \n",
      "iter = 220 ||∇f(.)|| = 0.0592 f(.) = 0.002041 \n",
      "iter = 221 ||∇f(.)|| = 0.0583 f(.) = 0.002006 \n",
      "iter = 222 ||∇f(.)|| = 0.0575 f(.) = 0.001973 \n",
      "iter = 223 ||∇f(.)|| = 0.0566 f(.) = 0.001940 \n",
      "iter = 224 ||∇f(.)|| = 0.0558 f(.) = 0.001908 \n",
      "iter = 225 ||∇f(.)|| = 0.0550 f(.) = 0.001877 \n",
      "iter = 226 ||∇f(.)|| = 0.0542 f(.) = 0.001847 \n",
      "iter = 227 ||∇f(.)|| = 0.0534 f(.) = 0.001818 \n",
      "iter = 228 ||∇f(.)|| = 0.0526 f(.) = 0.001790 \n",
      "iter = 229 ||∇f(.)|| = 0.0519 f(.) = 0.001762 \n",
      "iter = 230 ||∇f(.)|| = 0.0512 f(.) = 0.001735 \n",
      "iter = 231 ||∇f(.)|| = 0.0504 f(.) = 0.001709 \n",
      "iter = 232 ||∇f(.)|| = 0.0497 f(.) = 0.001684 \n",
      "iter = 233 ||∇f(.)|| = 0.0491 f(.) = 0.001660 \n",
      "iter = 234 ||∇f(.)|| = 0.0484 f(.) = 0.001636 \n",
      "iter = 235 ||∇f(.)|| = 0.0477 f(.) = 0.001612 \n",
      "iter = 236 ||∇f(.)|| = 0.0471 f(.) = 0.001590 \n",
      "iter = 237 ||∇f(.)|| = 0.0465 f(.) = 0.001568 \n",
      "iter = 238 ||∇f(.)|| = 0.0458 f(.) = 0.001546 \n",
      "iter = 239 ||∇f(.)|| = 0.0452 f(.) = 0.001526 \n",
      "iter = 240 ||∇f(.)|| = 0.0447 f(.) = 0.001505 \n",
      "iter = 241 ||∇f(.)|| = 0.0441 f(.) = 0.001485 \n",
      "iter = 242 ||∇f(.)|| = 0.0435 f(.) = 0.001466 \n",
      "iter = 243 ||∇f(.)|| = 0.0430 f(.) = 0.001447 \n",
      "iter = 244 ||∇f(.)|| = 0.0424 f(.) = 0.001429 \n",
      "iter = 245 ||∇f(.)|| = 0.0419 f(.) = 0.001411 \n",
      "iter = 246 ||∇f(.)|| = 0.0414 f(.) = 0.001394 \n",
      "iter = 247 ||∇f(.)|| = 0.0409 f(.) = 0.001377 \n",
      "iter = 248 ||∇f(.)|| = 0.0404 f(.) = 0.001360 \n",
      "iter = 249 ||∇f(.)|| = 0.0399 f(.) = 0.001344 \n",
      "iter = 250 ||∇f(.)|| = 0.0394 f(.) = 0.001328 \n",
      "iter = 251 ||∇f(.)|| = 0.0390 f(.) = 0.001312 \n",
      "iter = 252 ||∇f(.)|| = 0.0385 f(.) = 0.001297 \n",
      "iter = 253 ||∇f(.)|| = 0.0381 f(.) = 0.001283 \n",
      "iter = 254 ||∇f(.)|| = 0.0376 f(.) = 0.001268 \n",
      "iter = 255 ||∇f(.)|| = 0.0372 f(.) = 0.001254 \n",
      "iter = 256 ||∇f(.)|| = 0.0368 f(.) = 0.001240 \n",
      "iter = 257 ||∇f(.)|| = 0.0364 f(.) = 0.001227 \n",
      "iter = 258 ||∇f(.)|| = 0.0360 f(.) = 0.001214 \n",
      "iter = 259 ||∇f(.)|| = 0.0356 f(.) = 0.001201 \n",
      "iter = 260 ||∇f(.)|| = 0.0352 f(.) = 0.001188 \n",
      "iter = 261 ||∇f(.)|| = 0.0348 f(.) = 0.001176 \n",
      "iter = 262 ||∇f(.)|| = 0.0345 f(.) = 0.001164 \n",
      "iter = 263 ||∇f(.)|| = 0.0341 f(.) = 0.001152 \n",
      "iter = 264 ||∇f(.)|| = 0.0338 f(.) = 0.001140 \n",
      "iter = 265 ||∇f(.)|| = 0.0334 f(.) = 0.001129 \n",
      "iter = 266 ||∇f(.)|| = 0.0331 f(.) = 0.001118 \n",
      "iter = 267 ||∇f(.)|| = 0.0327 f(.) = 0.001107 \n",
      "iter = 268 ||∇f(.)|| = 0.0324 f(.) = 0.001096 \n",
      "iter = 269 ||∇f(.)|| = 0.0321 f(.) = 0.001086 \n",
      "iter = 270 ||∇f(.)|| = 0.0318 f(.) = 0.001076 \n",
      "iter = 271 ||∇f(.)|| = 0.0315 f(.) = 0.001066 \n",
      "iter = 272 ||∇f(.)|| = 0.0312 f(.) = 0.001056 \n",
      "iter = 273 ||∇f(.)|| = 0.0309 f(.) = 0.001046 \n",
      "iter = 274 ||∇f(.)|| = 0.0306 f(.) = 0.001037 \n",
      "iter = 275 ||∇f(.)|| = 0.0303 f(.) = 0.001027 \n",
      "iter = 276 ||∇f(.)|| = 0.0301 f(.) = 0.001018 \n",
      "iter = 277 ||∇f(.)|| = 0.0298 f(.) = 0.001009 \n",
      "iter = 278 ||∇f(.)|| = 0.0295 f(.) = 0.001000 \n",
      "iter = 279 ||∇f(.)|| = 0.0293 f(.) = 0.000992 \n",
      "iter = 280 ||∇f(.)|| = 0.0290 f(.) = 0.000983 \n",
      "iter = 281 ||∇f(.)|| = 0.0288 f(.) = 0.000975 \n",
      "iter = 282 ||∇f(.)|| = 0.0285 f(.) = 0.000966 \n",
      "iter = 283 ||∇f(.)|| = 0.0283 f(.) = 0.000958 \n",
      "iter = 284 ||∇f(.)|| = 0.0280 f(.) = 0.000950 \n",
      "iter = 285 ||∇f(.)|| = 0.0278 f(.) = 0.000943 \n",
      "iter = 286 ||∇f(.)|| = 0.0276 f(.) = 0.000935 \n",
      "iter = 287 ||∇f(.)|| = 0.0274 f(.) = 0.000927 \n",
      "iter = 288 ||∇f(.)|| = 0.0271 f(.) = 0.000920 \n",
      "iter = 289 ||∇f(.)|| = 0.0269 f(.) = 0.000912 \n",
      "iter = 290 ||∇f(.)|| = 0.0267 f(.) = 0.000905 \n",
      "iter = 291 ||∇f(.)|| = 0.0265 f(.) = 0.000898 \n",
      "iter = 292 ||∇f(.)|| = 0.0263 f(.) = 0.000891 \n",
      "iter = 293 ||∇f(.)|| = 0.0261 f(.) = 0.000884 \n",
      "iter = 294 ||∇f(.)|| = 0.0259 f(.) = 0.000877 \n",
      "iter = 295 ||∇f(.)|| = 0.0257 f(.) = 0.000871 \n",
      "iter = 296 ||∇f(.)|| = 0.0255 f(.) = 0.000864 \n",
      "iter = 297 ||∇f(.)|| = 0.0253 f(.) = 0.000858 \n",
      "iter = 298 ||∇f(.)|| = 0.0252 f(.) = 0.000851 \n",
      "iter = 299 ||∇f(.)|| = 0.0250 f(.) = 0.000845 \n",
      "iter = 300 ||∇f(.)|| = 0.0248 f(.) = 0.000839 \n",
      "iter = 301 ||∇f(.)|| = 0.0246 f(.) = 0.000833 \n",
      "iter = 302 ||∇f(.)|| = 0.0245 f(.) = 0.000827 \n",
      "iter = 303 ||∇f(.)|| = 0.0243 f(.) = 0.000821 \n",
      "iter = 304 ||∇f(.)|| = 0.0241 f(.) = 0.000815 \n",
      "iter = 305 ||∇f(.)|| = 0.0240 f(.) = 0.000809 \n",
      "iter = 306 ||∇f(.)|| = 0.0238 f(.) = 0.000803 \n",
      "iter = 307 ||∇f(.)|| = 0.0237 f(.) = 0.000798 \n",
      "iter = 308 ||∇f(.)|| = 0.0235 f(.) = 0.000792 \n",
      "iter = 309 ||∇f(.)|| = 0.0234 f(.) = 0.000786 \n",
      "iter = 310 ||∇f(.)|| = 0.0232 f(.) = 0.000781 \n",
      "iter = 311 ||∇f(.)|| = 0.0231 f(.) = 0.000776 \n",
      "iter = 312 ||∇f(.)|| = 0.0229 f(.) = 0.000770 \n",
      "iter = 313 ||∇f(.)|| = 0.0228 f(.) = 0.000765 \n",
      "iter = 314 ||∇f(.)|| = 0.0226 f(.) = 0.000760 \n",
      "iter = 315 ||∇f(.)|| = 0.0225 f(.) = 0.000755 \n",
      "iter = 316 ||∇f(.)|| = 0.0224 f(.) = 0.000750 \n",
      "iter = 317 ||∇f(.)|| = 0.0222 f(.) = 0.000745 \n",
      "iter = 318 ||∇f(.)|| = 0.0221 f(.) = 0.000740 \n",
      "iter = 319 ||∇f(.)|| = 0.0220 f(.) = 0.000735 \n",
      "iter = 320 ||∇f(.)|| = 0.0218 f(.) = 0.000730 \n",
      "iter = 321 ||∇f(.)|| = 0.0217 f(.) = 0.000726 \n",
      "iter = 322 ||∇f(.)|| = 0.0216 f(.) = 0.000721 \n",
      "iter = 323 ||∇f(.)|| = 0.0215 f(.) = 0.000716 \n",
      "iter = 324 ||∇f(.)|| = 0.0213 f(.) = 0.000712 \n",
      "iter = 325 ||∇f(.)|| = 0.0212 f(.) = 0.000707 \n",
      "iter = 326 ||∇f(.)|| = 0.0211 f(.) = 0.000703 \n",
      "iter = 327 ||∇f(.)|| = 0.0210 f(.) = 0.000698 \n",
      "iter = 328 ||∇f(.)|| = 0.0209 f(.) = 0.000694 \n",
      "iter = 329 ||∇f(.)|| = 0.0207 f(.) = 0.000689 \n",
      "iter = 330 ||∇f(.)|| = 0.0206 f(.) = 0.000685 \n",
      "iter = 331 ||∇f(.)|| = 0.0205 f(.) = 0.000681 \n",
      "iter = 332 ||∇f(.)|| = 0.0204 f(.) = 0.000677 \n",
      "iter = 333 ||∇f(.)|| = 0.0203 f(.) = 0.000672 \n",
      "iter = 334 ||∇f(.)|| = 0.0202 f(.) = 0.000668 \n",
      "iter = 335 ||∇f(.)|| = 0.0201 f(.) = 0.000664 \n",
      "iter = 336 ||∇f(.)|| = 0.0200 f(.) = 0.000660 \n",
      "iter = 337 ||∇f(.)|| = 0.0199 f(.) = 0.000656 \n",
      "iter = 338 ||∇f(.)|| = 0.0198 f(.) = 0.000652 \n",
      "iter = 339 ||∇f(.)|| = 0.0197 f(.) = 0.000648 \n",
      "iter = 340 ||∇f(.)|| = 0.0196 f(.) = 0.000645 \n",
      "iter = 341 ||∇f(.)|| = 0.0195 f(.) = 0.000641 \n",
      "iter = 342 ||∇f(.)|| = 0.0194 f(.) = 0.000637 \n",
      "iter = 343 ||∇f(.)|| = 0.0193 f(.) = 0.000633 \n",
      "iter = 344 ||∇f(.)|| = 0.0192 f(.) = 0.000629 \n",
      "iter = 345 ||∇f(.)|| = 0.0191 f(.) = 0.000626 \n",
      "iter = 346 ||∇f(.)|| = 0.0190 f(.) = 0.000622 \n",
      "iter = 347 ||∇f(.)|| = 0.0189 f(.) = 0.000619 \n",
      "iter = 348 ||∇f(.)|| = 0.0188 f(.) = 0.000615 \n",
      "iter = 349 ||∇f(.)|| = 0.0188 f(.) = 0.000611 \n",
      "iter = 350 ||∇f(.)|| = 0.0187 f(.) = 0.000608 \n",
      "iter = 351 ||∇f(.)|| = 0.0186 f(.) = 0.000604 \n",
      "iter = 352 ||∇f(.)|| = 0.0185 f(.) = 0.000601 \n",
      "iter = 353 ||∇f(.)|| = 0.0184 f(.) = 0.000598 \n",
      "iter = 354 ||∇f(.)|| = 0.0183 f(.) = 0.000594 \n",
      "iter = 355 ||∇f(.)|| = 0.0182 f(.) = 0.000591 \n",
      "iter = 356 ||∇f(.)|| = 0.0182 f(.) = 0.000588 \n",
      "iter = 357 ||∇f(.)|| = 0.0181 f(.) = 0.000584 \n",
      "iter = 358 ||∇f(.)|| = 0.0180 f(.) = 0.000581 \n",
      "iter = 359 ||∇f(.)|| = 0.0179 f(.) = 0.000578 \n",
      "iter = 360 ||∇f(.)|| = 0.0178 f(.) = 0.000575 \n",
      "iter = 361 ||∇f(.)|| = 0.0177 f(.) = 0.000571 \n",
      "iter = 362 ||∇f(.)|| = 0.0177 f(.) = 0.000568 \n",
      "iter = 363 ||∇f(.)|| = 0.0176 f(.) = 0.000565 \n",
      "iter = 364 ||∇f(.)|| = 0.0175 f(.) = 0.000562 \n",
      "iter = 365 ||∇f(.)|| = 0.0174 f(.) = 0.000559 \n",
      "iter = 366 ||∇f(.)|| = 0.0174 f(.) = 0.000556 \n",
      "iter = 367 ||∇f(.)|| = 0.0173 f(.) = 0.000553 \n",
      "iter = 368 ||∇f(.)|| = 0.0172 f(.) = 0.000550 \n",
      "iter = 369 ||∇f(.)|| = 0.0171 f(.) = 0.000547 \n",
      "iter = 370 ||∇f(.)|| = 0.0171 f(.) = 0.000544 \n",
      "iter = 371 ||∇f(.)|| = 0.0170 f(.) = 0.000541 \n",
      "iter = 372 ||∇f(.)|| = 0.0169 f(.) = 0.000538 \n",
      "iter = 373 ||∇f(.)|| = 0.0169 f(.) = 0.000535 \n",
      "iter = 374 ||∇f(.)|| = 0.0168 f(.) = 0.000533 \n",
      "iter = 375 ||∇f(.)|| = 0.0167 f(.) = 0.000530 \n",
      "iter = 376 ||∇f(.)|| = 0.0166 f(.) = 0.000527 \n",
      "iter = 377 ||∇f(.)|| = 0.0166 f(.) = 0.000524 \n",
      "iter = 378 ||∇f(.)|| = 0.0165 f(.) = 0.000521 \n",
      "iter = 379 ||∇f(.)|| = 0.0164 f(.) = 0.000519 \n",
      "iter = 380 ||∇f(.)|| = 0.0164 f(.) = 0.000516 \n",
      "iter = 381 ||∇f(.)|| = 0.0163 f(.) = 0.000513 \n",
      "iter = 382 ||∇f(.)|| = 0.0162 f(.) = 0.000511 \n",
      "iter = 383 ||∇f(.)|| = 0.0162 f(.) = 0.000508 \n",
      "iter = 384 ||∇f(.)|| = 0.0161 f(.) = 0.000506 \n",
      "iter = 385 ||∇f(.)|| = 0.0160 f(.) = 0.000503 \n",
      "iter = 386 ||∇f(.)|| = 0.0160 f(.) = 0.000500 \n",
      "iter = 387 ||∇f(.)|| = 0.0159 f(.) = 0.000498 \n",
      "iter = 388 ||∇f(.)|| = 0.0159 f(.) = 0.000495 \n",
      "iter = 389 ||∇f(.)|| = 0.0158 f(.) = 0.000493 \n",
      "iter = 390 ||∇f(.)|| = 0.0157 f(.) = 0.000490 \n",
      "iter = 391 ||∇f(.)|| = 0.0157 f(.) = 0.000488 \n",
      "iter = 392 ||∇f(.)|| = 0.0156 f(.) = 0.000485 \n",
      "iter = 393 ||∇f(.)|| = 0.0155 f(.) = 0.000483 \n",
      "iter = 394 ||∇f(.)|| = 0.0155 f(.) = 0.000481 \n",
      "iter = 395 ||∇f(.)|| = 0.0154 f(.) = 0.000478 \n",
      "iter = 396 ||∇f(.)|| = 0.0154 f(.) = 0.000476 \n",
      "iter = 397 ||∇f(.)|| = 0.0153 f(.) = 0.000473 \n",
      "iter = 398 ||∇f(.)|| = 0.0153 f(.) = 0.000471 \n",
      "iter = 399 ||∇f(.)|| = 0.0152 f(.) = 0.000469 \n",
      "iter = 400 ||∇f(.)|| = 0.0151 f(.) = 0.000466 \n",
      "iter = 401 ||∇f(.)|| = 0.0151 f(.) = 0.000464 \n",
      "iter = 402 ||∇f(.)|| = 0.0150 f(.) = 0.000462 \n",
      "iter = 403 ||∇f(.)|| = 0.0150 f(.) = 0.000460 \n",
      "iter = 404 ||∇f(.)|| = 0.0149 f(.) = 0.000457 \n",
      "iter = 405 ||∇f(.)|| = 0.0149 f(.) = 0.000455 \n",
      "iter = 406 ||∇f(.)|| = 0.0148 f(.) = 0.000453 \n",
      "iter = 407 ||∇f(.)|| = 0.0147 f(.) = 0.000451 \n",
      "iter = 408 ||∇f(.)|| = 0.0147 f(.) = 0.000449 \n",
      "iter = 409 ||∇f(.)|| = 0.0146 f(.) = 0.000446 \n",
      "iter = 410 ||∇f(.)|| = 0.0146 f(.) = 0.000444 \n",
      "iter = 411 ||∇f(.)|| = 0.0145 f(.) = 0.000442 \n",
      "iter = 412 ||∇f(.)|| = 0.0145 f(.) = 0.000440 \n",
      "iter = 413 ||∇f(.)|| = 0.0144 f(.) = 0.000438 \n",
      "iter = 414 ||∇f(.)|| = 0.0144 f(.) = 0.000436 \n",
      "iter = 415 ||∇f(.)|| = 0.0143 f(.) = 0.000434 \n",
      "iter = 416 ||∇f(.)|| = 0.0143 f(.) = 0.000432 \n",
      "iter = 417 ||∇f(.)|| = 0.0142 f(.) = 0.000430 \n",
      "iter = 418 ||∇f(.)|| = 0.0142 f(.) = 0.000428 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 419 ||∇f(.)|| = 0.0141 f(.) = 0.000426 \n",
      "iter = 420 ||∇f(.)|| = 0.0141 f(.) = 0.000424 \n",
      "iter = 421 ||∇f(.)|| = 0.0140 f(.) = 0.000422 \n",
      "iter = 422 ||∇f(.)|| = 0.0140 f(.) = 0.000420 \n",
      "iter = 423 ||∇f(.)|| = 0.0139 f(.) = 0.000418 \n",
      "iter = 424 ||∇f(.)|| = 0.0139 f(.) = 0.000416 \n",
      "iter = 425 ||∇f(.)|| = 0.0138 f(.) = 0.000414 \n",
      "iter = 426 ||∇f(.)|| = 0.0138 f(.) = 0.000412 \n",
      "iter = 427 ||∇f(.)|| = 0.0137 f(.) = 0.000410 \n",
      "iter = 428 ||∇f(.)|| = 0.0137 f(.) = 0.000408 \n",
      "iter = 429 ||∇f(.)|| = 0.0136 f(.) = 0.000406 \n",
      "iter = 430 ||∇f(.)|| = 0.0136 f(.) = 0.000405 \n",
      "iter = 431 ||∇f(.)|| = 0.0135 f(.) = 0.000403 \n",
      "iter = 432 ||∇f(.)|| = 0.0135 f(.) = 0.000401 \n",
      "iter = 433 ||∇f(.)|| = 0.0134 f(.) = 0.000399 \n",
      "iter = 434 ||∇f(.)|| = 0.0134 f(.) = 0.000397 \n",
      "iter = 435 ||∇f(.)|| = 0.0134 f(.) = 0.000395 \n",
      "iter = 436 ||∇f(.)|| = 0.0133 f(.) = 0.000394 \n",
      "iter = 437 ||∇f(.)|| = 0.0133 f(.) = 0.000392 \n",
      "iter = 438 ||∇f(.)|| = 0.0132 f(.) = 0.000390 \n",
      "iter = 439 ||∇f(.)|| = 0.0132 f(.) = 0.000388 \n",
      "iter = 440 ||∇f(.)|| = 0.0131 f(.) = 0.000387 \n",
      "iter = 441 ||∇f(.)|| = 0.0131 f(.) = 0.000385 \n",
      "iter = 442 ||∇f(.)|| = 0.0130 f(.) = 0.000383 \n",
      "iter = 443 ||∇f(.)|| = 0.0130 f(.) = 0.000382 \n",
      "iter = 444 ||∇f(.)|| = 0.0130 f(.) = 0.000380 \n",
      "iter = 445 ||∇f(.)|| = 0.0129 f(.) = 0.000378 \n",
      "iter = 446 ||∇f(.)|| = 0.0129 f(.) = 0.000377 \n",
      "iter = 447 ||∇f(.)|| = 0.0128 f(.) = 0.000375 \n",
      "iter = 448 ||∇f(.)|| = 0.0128 f(.) = 0.000373 \n",
      "iter = 449 ||∇f(.)|| = 0.0127 f(.) = 0.000372 \n",
      "iter = 450 ||∇f(.)|| = 0.0127 f(.) = 0.000370 \n",
      "iter = 451 ||∇f(.)|| = 0.0127 f(.) = 0.000368 \n",
      "iter = 452 ||∇f(.)|| = 0.0126 f(.) = 0.000367 \n",
      "iter = 453 ||∇f(.)|| = 0.0126 f(.) = 0.000365 \n",
      "iter = 454 ||∇f(.)|| = 0.0125 f(.) = 0.000364 \n",
      "iter = 455 ||∇f(.)|| = 0.0125 f(.) = 0.000362 \n",
      "iter = 456 ||∇f(.)|| = 0.0125 f(.) = 0.000361 \n",
      "iter = 457 ||∇f(.)|| = 0.0124 f(.) = 0.000359 \n",
      "iter = 458 ||∇f(.)|| = 0.0124 f(.) = 0.000357 \n",
      "iter = 459 ||∇f(.)|| = 0.0123 f(.) = 0.000356 \n",
      "iter = 460 ||∇f(.)|| = 0.0123 f(.) = 0.000354 \n",
      "iter = 461 ||∇f(.)|| = 0.0123 f(.) = 0.000353 \n",
      "iter = 462 ||∇f(.)|| = 0.0122 f(.) = 0.000351 \n",
      "iter = 463 ||∇f(.)|| = 0.0122 f(.) = 0.000350 \n",
      "iter = 464 ||∇f(.)|| = 0.0121 f(.) = 0.000348 \n",
      "iter = 465 ||∇f(.)|| = 0.0121 f(.) = 0.000347 \n",
      "iter = 466 ||∇f(.)|| = 0.0121 f(.) = 0.000345 \n",
      "iter = 467 ||∇f(.)|| = 0.0120 f(.) = 0.000344 \n",
      "iter = 468 ||∇f(.)|| = 0.0120 f(.) = 0.000343 \n",
      "iter = 469 ||∇f(.)|| = 0.0119 f(.) = 0.000341 \n",
      "iter = 470 ||∇f(.)|| = 0.0119 f(.) = 0.000340 \n",
      "iter = 471 ||∇f(.)|| = 0.0119 f(.) = 0.000338 \n",
      "iter = 472 ||∇f(.)|| = 0.0118 f(.) = 0.000337 \n",
      "iter = 473 ||∇f(.)|| = 0.0118 f(.) = 0.000336 \n",
      "iter = 474 ||∇f(.)|| = 0.0118 f(.) = 0.000334 \n",
      "iter = 475 ||∇f(.)|| = 0.0117 f(.) = 0.000333 \n",
      "iter = 476 ||∇f(.)|| = 0.0117 f(.) = 0.000331 \n",
      "iter = 477 ||∇f(.)|| = 0.0116 f(.) = 0.000330 \n",
      "iter = 478 ||∇f(.)|| = 0.0116 f(.) = 0.000329 \n",
      "iter = 479 ||∇f(.)|| = 0.0116 f(.) = 0.000327 \n",
      "iter = 480 ||∇f(.)|| = 0.0115 f(.) = 0.000326 \n",
      "iter = 481 ||∇f(.)|| = 0.0115 f(.) = 0.000325 \n",
      "iter = 482 ||∇f(.)|| = 0.0115 f(.) = 0.000323 \n",
      "iter = 483 ||∇f(.)|| = 0.0114 f(.) = 0.000322 \n",
      "iter = 484 ||∇f(.)|| = 0.0114 f(.) = 0.000321 \n",
      "iter = 485 ||∇f(.)|| = 0.0114 f(.) = 0.000319 \n",
      "iter = 486 ||∇f(.)|| = 0.0113 f(.) = 0.000318 \n",
      "iter = 487 ||∇f(.)|| = 0.0113 f(.) = 0.000317 \n",
      "iter = 488 ||∇f(.)|| = 0.0113 f(.) = 0.000316 \n",
      "iter = 489 ||∇f(.)|| = 0.0112 f(.) = 0.000314 \n",
      "iter = 490 ||∇f(.)|| = 0.0112 f(.) = 0.000313 \n",
      "iter = 491 ||∇f(.)|| = 0.0112 f(.) = 0.000312 \n",
      "iter = 492 ||∇f(.)|| = 0.0111 f(.) = 0.000311 \n",
      "iter = 493 ||∇f(.)|| = 0.0111 f(.) = 0.000309 \n",
      "iter = 494 ||∇f(.)|| = 0.0111 f(.) = 0.000308 \n",
      "iter = 495 ||∇f(.)|| = 0.0110 f(.) = 0.000307 \n",
      "iter = 496 ||∇f(.)|| = 0.0110 f(.) = 0.000306 \n",
      "iter = 497 ||∇f(.)|| = 0.0110 f(.) = 0.000304 \n",
      "iter = 498 ||∇f(.)|| = 0.0109 f(.) = 0.000303 \n",
      "iter = 499 ||∇f(.)|| = 0.0109 f(.) = 0.000302 \n",
      "iter = 500 ||∇f(.)|| = 0.0109 f(.) = 0.000301 \n",
      "iter = 501 ||∇f(.)|| = 0.0108 f(.) = 0.000300 \n",
      "iter = 502 ||∇f(.)|| = 0.0108 f(.) = 0.000298 \n",
      "iter = 503 ||∇f(.)|| = 0.0108 f(.) = 0.000297 \n",
      "iter = 504 ||∇f(.)|| = 0.0107 f(.) = 0.000296 \n",
      "iter = 505 ||∇f(.)|| = 0.0107 f(.) = 0.000295 \n",
      "iter = 506 ||∇f(.)|| = 0.0107 f(.) = 0.000294 \n",
      "iter = 507 ||∇f(.)|| = 0.0106 f(.) = 0.000293 \n",
      "iter = 508 ||∇f(.)|| = 0.0106 f(.) = 0.000292 \n",
      "iter = 509 ||∇f(.)|| = 0.0106 f(.) = 0.000290 \n",
      "iter = 510 ||∇f(.)|| = 0.0106 f(.) = 0.000289 \n",
      "iter = 511 ||∇f(.)|| = 0.0105 f(.) = 0.000288 \n",
      "iter = 512 ||∇f(.)|| = 0.0105 f(.) = 0.000287 \n",
      "iter = 513 ||∇f(.)|| = 0.0105 f(.) = 0.000286 \n",
      "iter = 514 ||∇f(.)|| = 0.0104 f(.) = 0.000285 \n",
      "iter = 515 ||∇f(.)|| = 0.0104 f(.) = 0.000284 \n",
      "iter = 516 ||∇f(.)|| = 0.0104 f(.) = 0.000283 \n",
      "iter = 517 ||∇f(.)|| = 0.0103 f(.) = 0.000282 \n",
      "iter = 518 ||∇f(.)|| = 0.0103 f(.) = 0.000281 \n",
      "iter = 519 ||∇f(.)|| = 0.0103 f(.) = 0.000280 \n",
      "iter = 520 ||∇f(.)|| = 0.0103 f(.) = 0.000279 \n",
      "iter = 521 ||∇f(.)|| = 0.0102 f(.) = 0.000277 \n",
      "iter = 522 ||∇f(.)|| = 0.0102 f(.) = 0.000276 \n",
      "iter = 523 ||∇f(.)|| = 0.0102 f(.) = 0.000275 \n",
      "iter = 524 ||∇f(.)|| = 0.0101 f(.) = 0.000274 \n",
      "iter = 525 ||∇f(.)|| = 0.0101 f(.) = 0.000273 \n",
      "iter = 526 ||∇f(.)|| = 0.0101 f(.) = 0.000272 \n",
      "iter = 527 ||∇f(.)|| = 0.0101 f(.) = 0.000271 \n",
      "iter = 528 ||∇f(.)|| = 0.0100 f(.) = 0.000270 \n",
      "iter = 529 ||∇f(.)|| = 0.0100 f(.) = 0.000269 \n",
      "iter = 530 ||∇f(.)|| = 0.0100 f(.) = 0.000268 \n",
      "iter = 531 ||∇f(.)|| = 0.0099 f(.) = 0.000267 \n",
      "iter = 532 ||∇f(.)|| = 0.0099 f(.) = 0.000266 \n",
      "iter = 533 ||∇f(.)|| = 0.0099 f(.) = 0.000265 \n",
      "iter = 534 ||∇f(.)|| = 0.0099 f(.) = 0.000264 \n",
      "iter = 535 ||∇f(.)|| = 0.0098 f(.) = 0.000263 \n",
      "iter = 536 ||∇f(.)|| = 0.0098 f(.) = 0.000262 \n",
      "iter = 537 ||∇f(.)|| = 0.0098 f(.) = 0.000261 \n",
      "iter = 538 ||∇f(.)|| = 0.0098 f(.) = 0.000260 \n",
      "iter = 539 ||∇f(.)|| = 0.0097 f(.) = 0.000260 \n",
      "iter = 540 ||∇f(.)|| = 0.0097 f(.) = 0.000259 \n",
      "iter = 541 ||∇f(.)|| = 0.0097 f(.) = 0.000258 \n",
      "iter = 542 ||∇f(.)|| = 0.0096 f(.) = 0.000257 \n",
      "iter = 543 ||∇f(.)|| = 0.0096 f(.) = 0.000256 \n",
      "iter = 544 ||∇f(.)|| = 0.0096 f(.) = 0.000255 \n",
      "iter = 545 ||∇f(.)|| = 0.0096 f(.) = 0.000254 \n",
      "iter = 546 ||∇f(.)|| = 0.0095 f(.) = 0.000253 \n",
      "iter = 547 ||∇f(.)|| = 0.0095 f(.) = 0.000252 \n",
      "iter = 548 ||∇f(.)|| = 0.0095 f(.) = 0.000251 \n",
      "iter = 549 ||∇f(.)|| = 0.0095 f(.) = 0.000250 \n",
      "iter = 550 ||∇f(.)|| = 0.0094 f(.) = 0.000249 \n",
      "iter = 551 ||∇f(.)|| = 0.0094 f(.) = 0.000249 \n",
      "iter = 552 ||∇f(.)|| = 0.0094 f(.) = 0.000248 \n",
      "iter = 553 ||∇f(.)|| = 0.0094 f(.) = 0.000247 \n",
      "iter = 554 ||∇f(.)|| = 0.0093 f(.) = 0.000246 \n",
      "iter = 555 ||∇f(.)|| = 0.0093 f(.) = 0.000245 \n",
      "iter = 556 ||∇f(.)|| = 0.0093 f(.) = 0.000244 \n",
      "iter = 557 ||∇f(.)|| = 0.0093 f(.) = 0.000243 \n",
      "iter = 558 ||∇f(.)|| = 0.0092 f(.) = 0.000242 \n",
      "iter = 559 ||∇f(.)|| = 0.0092 f(.) = 0.000242 \n",
      "iter = 560 ||∇f(.)|| = 0.0092 f(.) = 0.000241 \n",
      "iter = 561 ||∇f(.)|| = 0.0092 f(.) = 0.000240 \n",
      "iter = 562 ||∇f(.)|| = 0.0091 f(.) = 0.000239 \n",
      "iter = 563 ||∇f(.)|| = 0.0091 f(.) = 0.000238 \n",
      "iter = 564 ||∇f(.)|| = 0.0091 f(.) = 0.000237 \n",
      "iter = 565 ||∇f(.)|| = 0.0091 f(.) = 0.000237 \n",
      "iter = 566 ||∇f(.)|| = 0.0090 f(.) = 0.000236 \n",
      "iter = 567 ||∇f(.)|| = 0.0090 f(.) = 0.000235 \n",
      "iter = 568 ||∇f(.)|| = 0.0090 f(.) = 0.000234 \n",
      "iter = 569 ||∇f(.)|| = 0.0090 f(.) = 0.000233 \n",
      "iter = 570 ||∇f(.)|| = 0.0090 f(.) = 0.000232 \n",
      "iter = 571 ||∇f(.)|| = 0.0089 f(.) = 0.000232 \n",
      "iter = 572 ||∇f(.)|| = 0.0089 f(.) = 0.000231 \n",
      "iter = 573 ||∇f(.)|| = 0.0089 f(.) = 0.000230 \n",
      "iter = 574 ||∇f(.)|| = 0.0089 f(.) = 0.000229 \n",
      "iter = 575 ||∇f(.)|| = 0.0088 f(.) = 0.000229 \n",
      "iter = 576 ||∇f(.)|| = 0.0088 f(.) = 0.000228 \n",
      "iter = 577 ||∇f(.)|| = 0.0088 f(.) = 0.000227 \n",
      "iter = 578 ||∇f(.)|| = 0.0088 f(.) = 0.000226 \n",
      "iter = 579 ||∇f(.)|| = 0.0088 f(.) = 0.000225 \n",
      "iter = 580 ||∇f(.)|| = 0.0087 f(.) = 0.000225 \n",
      "iter = 581 ||∇f(.)|| = 0.0087 f(.) = 0.000224 \n",
      "iter = 582 ||∇f(.)|| = 0.0087 f(.) = 0.000223 \n",
      "iter = 583 ||∇f(.)|| = 0.0087 f(.) = 0.000222 \n",
      "iter = 584 ||∇f(.)|| = 0.0086 f(.) = 0.000222 \n",
      "iter = 585 ||∇f(.)|| = 0.0086 f(.) = 0.000221 \n",
      "iter = 586 ||∇f(.)|| = 0.0086 f(.) = 0.000220 \n",
      "iter = 587 ||∇f(.)|| = 0.0086 f(.) = 0.000219 \n",
      "iter = 588 ||∇f(.)|| = 0.0086 f(.) = 0.000219 \n",
      "iter = 589 ||∇f(.)|| = 0.0085 f(.) = 0.000218 \n",
      "iter = 590 ||∇f(.)|| = 0.0085 f(.) = 0.000217 \n",
      "iter = 591 ||∇f(.)|| = 0.0085 f(.) = 0.000216 \n",
      "iter = 592 ||∇f(.)|| = 0.0085 f(.) = 0.000216 \n",
      "iter = 593 ||∇f(.)|| = 0.0084 f(.) = 0.000215 \n",
      "iter = 594 ||∇f(.)|| = 0.0084 f(.) = 0.000214 \n",
      "iter = 595 ||∇f(.)|| = 0.0084 f(.) = 0.000214 \n",
      "iter = 596 ||∇f(.)|| = 0.0084 f(.) = 0.000213 \n",
      "iter = 597 ||∇f(.)|| = 0.0084 f(.) = 0.000212 \n",
      "iter = 598 ||∇f(.)|| = 0.0083 f(.) = 0.000212 \n",
      "iter = 599 ||∇f(.)|| = 0.0083 f(.) = 0.000211 \n",
      "iter = 600 ||∇f(.)|| = 0.0083 f(.) = 0.000210 \n",
      "iter = 601 ||∇f(.)|| = 0.0083 f(.) = 0.000209 \n",
      "iter = 602 ||∇f(.)|| = 0.0083 f(.) = 0.000209 \n",
      "iter = 603 ||∇f(.)|| = 0.0082 f(.) = 0.000208 \n",
      "iter = 604 ||∇f(.)|| = 0.0082 f(.) = 0.000207 \n",
      "iter = 605 ||∇f(.)|| = 0.0082 f(.) = 0.000207 \n",
      "iter = 606 ||∇f(.)|| = 0.0082 f(.) = 0.000206 \n",
      "iter = 607 ||∇f(.)|| = 0.0082 f(.) = 0.000205 \n",
      "iter = 608 ||∇f(.)|| = 0.0081 f(.) = 0.000205 \n",
      "iter = 609 ||∇f(.)|| = 0.0081 f(.) = 0.000204 \n",
      "iter = 610 ||∇f(.)|| = 0.0081 f(.) = 0.000203 \n",
      "iter = 611 ||∇f(.)|| = 0.0081 f(.) = 0.000203 \n",
      "iter = 612 ||∇f(.)|| = 0.0081 f(.) = 0.000202 \n",
      "iter = 613 ||∇f(.)|| = 0.0080 f(.) = 0.000201 \n",
      "iter = 614 ||∇f(.)|| = 0.0080 f(.) = 0.000201 \n",
      "iter = 615 ||∇f(.)|| = 0.0080 f(.) = 0.000200 \n",
      "iter = 616 ||∇f(.)|| = 0.0080 f(.) = 0.000200 \n",
      "iter = 617 ||∇f(.)|| = 0.0080 f(.) = 0.000199 \n",
      "iter = 618 ||∇f(.)|| = 0.0079 f(.) = 0.000198 \n",
      "iter = 619 ||∇f(.)|| = 0.0079 f(.) = 0.000198 \n",
      "iter = 620 ||∇f(.)|| = 0.0079 f(.) = 0.000197 \n",
      "iter = 621 ||∇f(.)|| = 0.0079 f(.) = 0.000196 \n",
      "iter = 622 ||∇f(.)|| = 0.0079 f(.) = 0.000196 \n",
      "iter = 623 ||∇f(.)|| = 0.0079 f(.) = 0.000195 \n",
      "iter = 624 ||∇f(.)|| = 0.0078 f(.) = 0.000195 \n",
      "iter = 625 ||∇f(.)|| = 0.0078 f(.) = 0.000194 \n",
      "iter = 626 ||∇f(.)|| = 0.0078 f(.) = 0.000193 \n",
      "iter = 627 ||∇f(.)|| = 0.0078 f(.) = 0.000193 \n",
      "iter = 628 ||∇f(.)|| = 0.0078 f(.) = 0.000192 \n",
      "iter = 629 ||∇f(.)|| = 0.0077 f(.) = 0.000191 \n",
      "iter = 630 ||∇f(.)|| = 0.0077 f(.) = 0.000191 \n",
      "iter = 631 ||∇f(.)|| = 0.0077 f(.) = 0.000190 \n",
      "iter = 632 ||∇f(.)|| = 0.0077 f(.) = 0.000190 \n",
      "iter = 633 ||∇f(.)|| = 0.0077 f(.) = 0.000189 \n",
      "iter = 634 ||∇f(.)|| = 0.0077 f(.) = 0.000189 \n",
      "iter = 635 ||∇f(.)|| = 0.0076 f(.) = 0.000188 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 636 ||∇f(.)|| = 0.0076 f(.) = 0.000187 \n",
      "iter = 637 ||∇f(.)|| = 0.0076 f(.) = 0.000187 \n",
      "iter = 638 ||∇f(.)|| = 0.0076 f(.) = 0.000186 \n",
      "iter = 639 ||∇f(.)|| = 0.0076 f(.) = 0.000186 \n",
      "iter = 640 ||∇f(.)|| = 0.0075 f(.) = 0.000185 \n",
      "iter = 641 ||∇f(.)|| = 0.0075 f(.) = 0.000184 \n",
      "iter = 642 ||∇f(.)|| = 0.0075 f(.) = 0.000184 \n",
      "iter = 643 ||∇f(.)|| = 0.0075 f(.) = 0.000183 \n",
      "iter = 644 ||∇f(.)|| = 0.0075 f(.) = 0.000183 \n",
      "iter = 645 ||∇f(.)|| = 0.0075 f(.) = 0.000182 \n",
      "iter = 646 ||∇f(.)|| = 0.0074 f(.) = 0.000182 \n",
      "iter = 647 ||∇f(.)|| = 0.0074 f(.) = 0.000181 \n",
      "iter = 648 ||∇f(.)|| = 0.0074 f(.) = 0.000181 \n",
      "iter = 649 ||∇f(.)|| = 0.0074 f(.) = 0.000180 \n",
      "iter = 650 ||∇f(.)|| = 0.0074 f(.) = 0.000179 \n",
      "iter = 651 ||∇f(.)|| = 0.0074 f(.) = 0.000179 \n",
      "iter = 652 ||∇f(.)|| = 0.0073 f(.) = 0.000178 \n",
      "iter = 653 ||∇f(.)|| = 0.0073 f(.) = 0.000178 \n",
      "iter = 654 ||∇f(.)|| = 0.0073 f(.) = 0.000177 \n",
      "iter = 655 ||∇f(.)|| = 0.0073 f(.) = 0.000177 \n",
      "iter = 656 ||∇f(.)|| = 0.0073 f(.) = 0.000176 \n",
      "iter = 657 ||∇f(.)|| = 0.0073 f(.) = 0.000176 \n",
      "iter = 658 ||∇f(.)|| = 0.0072 f(.) = 0.000175 \n",
      "iter = 659 ||∇f(.)|| = 0.0072 f(.) = 0.000175 \n",
      "iter = 660 ||∇f(.)|| = 0.0072 f(.) = 0.000174 \n",
      "iter = 661 ||∇f(.)|| = 0.0072 f(.) = 0.000174 \n",
      "iter = 662 ||∇f(.)|| = 0.0072 f(.) = 0.000173 \n",
      "iter = 663 ||∇f(.)|| = 0.0072 f(.) = 0.000173 \n",
      "iter = 664 ||∇f(.)|| = 0.0071 f(.) = 0.000172 \n",
      "iter = 665 ||∇f(.)|| = 0.0071 f(.) = 0.000172 \n",
      "iter = 666 ||∇f(.)|| = 0.0071 f(.) = 0.000171 \n",
      "iter = 667 ||∇f(.)|| = 0.0071 f(.) = 0.000171 \n",
      "iter = 668 ||∇f(.)|| = 0.0071 f(.) = 0.000170 \n",
      "iter = 669 ||∇f(.)|| = 0.0071 f(.) = 0.000170 \n",
      "iter = 670 ||∇f(.)|| = 0.0071 f(.) = 0.000169 \n",
      "iter = 671 ||∇f(.)|| = 0.0070 f(.) = 0.000169 \n",
      "iter = 672 ||∇f(.)|| = 0.0070 f(.) = 0.000168 \n",
      "iter = 673 ||∇f(.)|| = 0.0070 f(.) = 0.000168 \n",
      "iter = 674 ||∇f(.)|| = 0.0070 f(.) = 0.000167 \n",
      "iter = 675 ||∇f(.)|| = 0.0070 f(.) = 0.000167 \n",
      "iter = 676 ||∇f(.)|| = 0.0070 f(.) = 0.000166 \n",
      "iter = 677 ||∇f(.)|| = 0.0069 f(.) = 0.000166 \n",
      "iter = 678 ||∇f(.)|| = 0.0069 f(.) = 0.000165 \n",
      "iter = 679 ||∇f(.)|| = 0.0069 f(.) = 0.000165 \n",
      "iter = 680 ||∇f(.)|| = 0.0069 f(.) = 0.000164 \n",
      "iter = 681 ||∇f(.)|| = 0.0069 f(.) = 0.000164 \n",
      "iter = 682 ||∇f(.)|| = 0.0069 f(.) = 0.000163 \n",
      "iter = 683 ||∇f(.)|| = 0.0069 f(.) = 0.000163 \n",
      "iter = 684 ||∇f(.)|| = 0.0068 f(.) = 0.000162 \n",
      "iter = 685 ||∇f(.)|| = 0.0068 f(.) = 0.000162 \n",
      "iter = 686 ||∇f(.)|| = 0.0068 f(.) = 0.000161 \n",
      "iter = 687 ||∇f(.)|| = 0.0068 f(.) = 0.000161 \n",
      "iter = 688 ||∇f(.)|| = 0.0068 f(.) = 0.000160 \n",
      "iter = 689 ||∇f(.)|| = 0.0068 f(.) = 0.000160 \n",
      "iter = 690 ||∇f(.)|| = 0.0068 f(.) = 0.000160 \n",
      "iter = 691 ||∇f(.)|| = 0.0067 f(.) = 0.000159 \n",
      "iter = 692 ||∇f(.)|| = 0.0067 f(.) = 0.000159 \n",
      "iter = 693 ||∇f(.)|| = 0.0067 f(.) = 0.000158 \n",
      "iter = 694 ||∇f(.)|| = 0.0067 f(.) = 0.000158 \n",
      "iter = 695 ||∇f(.)|| = 0.0067 f(.) = 0.000157 \n",
      "iter = 696 ||∇f(.)|| = 0.0067 f(.) = 0.000157 \n",
      "iter = 697 ||∇f(.)|| = 0.0067 f(.) = 0.000156 \n",
      "iter = 698 ||∇f(.)|| = 0.0066 f(.) = 0.000156 \n",
      "iter = 699 ||∇f(.)|| = 0.0066 f(.) = 0.000155 \n",
      "iter = 700 ||∇f(.)|| = 0.0066 f(.) = 0.000155 \n",
      "iter = 701 ||∇f(.)|| = 0.0066 f(.) = 0.000155 \n",
      "iter = 702 ||∇f(.)|| = 0.0066 f(.) = 0.000154 \n",
      "iter = 703 ||∇f(.)|| = 0.0066 f(.) = 0.000154 \n",
      "iter = 704 ||∇f(.)|| = 0.0066 f(.) = 0.000153 \n",
      "iter = 705 ||∇f(.)|| = 0.0065 f(.) = 0.000153 \n",
      "iter = 706 ||∇f(.)|| = 0.0065 f(.) = 0.000152 \n",
      "iter = 707 ||∇f(.)|| = 0.0065 f(.) = 0.000152 \n",
      "iter = 708 ||∇f(.)|| = 0.0065 f(.) = 0.000152 \n",
      "iter = 709 ||∇f(.)|| = 0.0065 f(.) = 0.000151 \n",
      "iter = 710 ||∇f(.)|| = 0.0065 f(.) = 0.000151 \n",
      "iter = 711 ||∇f(.)|| = 0.0065 f(.) = 0.000150 \n",
      "iter = 712 ||∇f(.)|| = 0.0064 f(.) = 0.000150 \n",
      "iter = 713 ||∇f(.)|| = 0.0064 f(.) = 0.000150 \n",
      "iter = 714 ||∇f(.)|| = 0.0064 f(.) = 0.000149 \n",
      "iter = 715 ||∇f(.)|| = 0.0064 f(.) = 0.000149 \n",
      "iter = 716 ||∇f(.)|| = 0.0064 f(.) = 0.000148 \n",
      "iter = 717 ||∇f(.)|| = 0.0064 f(.) = 0.000148 \n",
      "iter = 718 ||∇f(.)|| = 0.0064 f(.) = 0.000147 \n",
      "iter = 719 ||∇f(.)|| = 0.0064 f(.) = 0.000147 \n",
      "iter = 720 ||∇f(.)|| = 0.0063 f(.) = 0.000147 \n",
      "iter = 721 ||∇f(.)|| = 0.0063 f(.) = 0.000146 \n",
      "iter = 722 ||∇f(.)|| = 0.0063 f(.) = 0.000146 \n",
      "iter = 723 ||∇f(.)|| = 0.0063 f(.) = 0.000145 \n",
      "iter = 724 ||∇f(.)|| = 0.0063 f(.) = 0.000145 \n",
      "iter = 725 ||∇f(.)|| = 0.0063 f(.) = 0.000145 \n",
      "iter = 726 ||∇f(.)|| = 0.0063 f(.) = 0.000144 \n",
      "iter = 727 ||∇f(.)|| = 0.0062 f(.) = 0.000144 \n",
      "iter = 728 ||∇f(.)|| = 0.0062 f(.) = 0.000143 \n",
      "iter = 729 ||∇f(.)|| = 0.0062 f(.) = 0.000143 \n",
      "iter = 730 ||∇f(.)|| = 0.0062 f(.) = 0.000143 \n",
      "iter = 731 ||∇f(.)|| = 0.0062 f(.) = 0.000142 \n",
      "iter = 732 ||∇f(.)|| = 0.0062 f(.) = 0.000142 \n",
      "iter = 733 ||∇f(.)|| = 0.0062 f(.) = 0.000142 \n",
      "iter = 734 ||∇f(.)|| = 0.0062 f(.) = 0.000141 \n",
      "iter = 735 ||∇f(.)|| = 0.0061 f(.) = 0.000141 \n",
      "iter = 736 ||∇f(.)|| = 0.0061 f(.) = 0.000140 \n",
      "iter = 737 ||∇f(.)|| = 0.0061 f(.) = 0.000140 \n",
      "iter = 738 ||∇f(.)|| = 0.0061 f(.) = 0.000140 \n",
      "iter = 739 ||∇f(.)|| = 0.0061 f(.) = 0.000139 \n",
      "iter = 740 ||∇f(.)|| = 0.0061 f(.) = 0.000139 \n",
      "iter = 741 ||∇f(.)|| = 0.0061 f(.) = 0.000139 \n",
      "iter = 742 ||∇f(.)|| = 0.0061 f(.) = 0.000138 \n",
      "iter = 743 ||∇f(.)|| = 0.0061 f(.) = 0.000138 \n",
      "iter = 744 ||∇f(.)|| = 0.0060 f(.) = 0.000137 \n",
      "iter = 745 ||∇f(.)|| = 0.0060 f(.) = 0.000137 \n",
      "iter = 746 ||∇f(.)|| = 0.0060 f(.) = 0.000137 \n",
      "iter = 747 ||∇f(.)|| = 0.0060 f(.) = 0.000136 \n",
      "iter = 748 ||∇f(.)|| = 0.0060 f(.) = 0.000136 \n",
      "iter = 749 ||∇f(.)|| = 0.0060 f(.) = 0.000136 \n",
      "iter = 750 ||∇f(.)|| = 0.0060 f(.) = 0.000135 \n",
      "iter = 751 ||∇f(.)|| = 0.0060 f(.) = 0.000135 \n",
      "iter = 752 ||∇f(.)|| = 0.0059 f(.) = 0.000135 \n",
      "iter = 753 ||∇f(.)|| = 0.0059 f(.) = 0.000134 \n",
      "iter = 754 ||∇f(.)|| = 0.0059 f(.) = 0.000134 \n",
      "iter = 755 ||∇f(.)|| = 0.0059 f(.) = 0.000134 \n",
      "iter = 756 ||∇f(.)|| = 0.0059 f(.) = 0.000133 \n",
      "iter = 757 ||∇f(.)|| = 0.0059 f(.) = 0.000133 \n",
      "iter = 758 ||∇f(.)|| = 0.0059 f(.) = 0.000132 \n",
      "iter = 759 ||∇f(.)|| = 0.0059 f(.) = 0.000132 \n",
      "iter = 760 ||∇f(.)|| = 0.0059 f(.) = 0.000132 \n",
      "iter = 761 ||∇f(.)|| = 0.0058 f(.) = 0.000131 \n",
      "iter = 762 ||∇f(.)|| = 0.0058 f(.) = 0.000131 \n",
      "iter = 763 ||∇f(.)|| = 0.0058 f(.) = 0.000131 \n",
      "iter = 764 ||∇f(.)|| = 0.0058 f(.) = 0.000130 \n",
      "iter = 765 ||∇f(.)|| = 0.0058 f(.) = 0.000130 \n",
      "iter = 766 ||∇f(.)|| = 0.0058 f(.) = 0.000130 \n",
      "iter = 767 ||∇f(.)|| = 0.0058 f(.) = 0.000129 \n",
      "iter = 768 ||∇f(.)|| = 0.0058 f(.) = 0.000129 \n",
      "iter = 769 ||∇f(.)|| = 0.0057 f(.) = 0.000129 \n",
      "iter = 770 ||∇f(.)|| = 0.0057 f(.) = 0.000128 \n",
      "iter = 771 ||∇f(.)|| = 0.0057 f(.) = 0.000128 \n",
      "iter = 772 ||∇f(.)|| = 0.0057 f(.) = 0.000128 \n",
      "iter = 773 ||∇f(.)|| = 0.0057 f(.) = 0.000127 \n",
      "iter = 774 ||∇f(.)|| = 0.0057 f(.) = 0.000127 \n",
      "iter = 775 ||∇f(.)|| = 0.0057 f(.) = 0.000127 \n",
      "iter = 776 ||∇f(.)|| = 0.0057 f(.) = 0.000126 \n",
      "iter = 777 ||∇f(.)|| = 0.0057 f(.) = 0.000126 \n",
      "iter = 778 ||∇f(.)|| = 0.0057 f(.) = 0.000126 \n",
      "iter = 779 ||∇f(.)|| = 0.0056 f(.) = 0.000126 \n",
      "iter = 780 ||∇f(.)|| = 0.0056 f(.) = 0.000125 \n",
      "iter = 781 ||∇f(.)|| = 0.0056 f(.) = 0.000125 \n",
      "iter = 782 ||∇f(.)|| = 0.0056 f(.) = 0.000125 \n",
      "iter = 783 ||∇f(.)|| = 0.0056 f(.) = 0.000124 \n",
      "iter = 784 ||∇f(.)|| = 0.0056 f(.) = 0.000124 \n",
      "iter = 785 ||∇f(.)|| = 0.0056 f(.) = 0.000124 \n",
      "iter = 786 ||∇f(.)|| = 0.0056 f(.) = 0.000123 \n",
      "iter = 787 ||∇f(.)|| = 0.0056 f(.) = 0.000123 \n",
      "iter = 788 ||∇f(.)|| = 0.0055 f(.) = 0.000123 \n",
      "iter = 789 ||∇f(.)|| = 0.0055 f(.) = 0.000122 \n",
      "iter = 790 ||∇f(.)|| = 0.0055 f(.) = 0.000122 \n",
      "iter = 791 ||∇f(.)|| = 0.0055 f(.) = 0.000122 \n",
      "iter = 792 ||∇f(.)|| = 0.0055 f(.) = 0.000121 \n",
      "iter = 793 ||∇f(.)|| = 0.0055 f(.) = 0.000121 \n",
      "iter = 794 ||∇f(.)|| = 0.0055 f(.) = 0.000121 \n",
      "iter = 795 ||∇f(.)|| = 0.0055 f(.) = 0.000121 \n",
      "iter = 796 ||∇f(.)|| = 0.0055 f(.) = 0.000120 \n",
      "iter = 797 ||∇f(.)|| = 0.0055 f(.) = 0.000120 \n",
      "iter = 798 ||∇f(.)|| = 0.0054 f(.) = 0.000120 \n",
      "iter = 799 ||∇f(.)|| = 0.0054 f(.) = 0.000119 \n",
      "iter = 800 ||∇f(.)|| = 0.0054 f(.) = 0.000119 \n",
      "iter = 801 ||∇f(.)|| = 0.0054 f(.) = 0.000119 \n",
      "iter = 802 ||∇f(.)|| = 0.0054 f(.) = 0.000119 \n",
      "iter = 803 ||∇f(.)|| = 0.0054 f(.) = 0.000118 \n",
      "iter = 804 ||∇f(.)|| = 0.0054 f(.) = 0.000118 \n",
      "iter = 805 ||∇f(.)|| = 0.0054 f(.) = 0.000118 \n",
      "iter = 806 ||∇f(.)|| = 0.0054 f(.) = 0.000117 \n",
      "iter = 807 ||∇f(.)|| = 0.0054 f(.) = 0.000117 \n",
      "iter = 808 ||∇f(.)|| = 0.0053 f(.) = 0.000117 \n",
      "iter = 809 ||∇f(.)|| = 0.0053 f(.) = 0.000116 \n",
      "iter = 810 ||∇f(.)|| = 0.0053 f(.) = 0.000116 \n",
      "iter = 811 ||∇f(.)|| = 0.0053 f(.) = 0.000116 \n",
      "iter = 812 ||∇f(.)|| = 0.0053 f(.) = 0.000116 \n",
      "iter = 813 ||∇f(.)|| = 0.0053 f(.) = 0.000115 \n",
      "iter = 814 ||∇f(.)|| = 0.0053 f(.) = 0.000115 \n",
      "iter = 815 ||∇f(.)|| = 0.0053 f(.) = 0.000115 \n",
      "iter = 816 ||∇f(.)|| = 0.0053 f(.) = 0.000115 \n",
      "iter = 817 ||∇f(.)|| = 0.0053 f(.) = 0.000114 \n",
      "iter = 818 ||∇f(.)|| = 0.0052 f(.) = 0.000114 \n",
      "iter = 819 ||∇f(.)|| = 0.0052 f(.) = 0.000114 \n",
      "iter = 820 ||∇f(.)|| = 0.0052 f(.) = 0.000113 \n",
      "iter = 821 ||∇f(.)|| = 0.0052 f(.) = 0.000113 \n",
      "iter = 822 ||∇f(.)|| = 0.0052 f(.) = 0.000113 \n",
      "iter = 823 ||∇f(.)|| = 0.0052 f(.) = 0.000113 \n",
      "iter = 824 ||∇f(.)|| = 0.0052 f(.) = 0.000112 \n",
      "iter = 825 ||∇f(.)|| = 0.0052 f(.) = 0.000112 \n",
      "iter = 826 ||∇f(.)|| = 0.0052 f(.) = 0.000112 \n",
      "iter = 827 ||∇f(.)|| = 0.0052 f(.) = 0.000112 \n",
      "iter = 828 ||∇f(.)|| = 0.0052 f(.) = 0.000111 \n",
      "iter = 829 ||∇f(.)|| = 0.0051 f(.) = 0.000111 \n",
      "iter = 830 ||∇f(.)|| = 0.0051 f(.) = 0.000111 \n",
      "iter = 831 ||∇f(.)|| = 0.0051 f(.) = 0.000110 \n",
      "iter = 832 ||∇f(.)|| = 0.0051 f(.) = 0.000110 \n",
      "iter = 833 ||∇f(.)|| = 0.0051 f(.) = 0.000110 \n",
      "iter = 834 ||∇f(.)|| = 0.0051 f(.) = 0.000110 \n",
      "iter = 835 ||∇f(.)|| = 0.0051 f(.) = 0.000109 \n",
      "iter = 836 ||∇f(.)|| = 0.0051 f(.) = 0.000109 \n",
      "iter = 837 ||∇f(.)|| = 0.0051 f(.) = 0.000109 \n",
      "iter = 838 ||∇f(.)|| = 0.0051 f(.) = 0.000109 \n",
      "iter = 839 ||∇f(.)|| = 0.0051 f(.) = 0.000108 \n",
      "iter = 840 ||∇f(.)|| = 0.0050 f(.) = 0.000108 \n",
      "iter = 841 ||∇f(.)|| = 0.0050 f(.) = 0.000108 \n",
      "iter = 842 ||∇f(.)|| = 0.0050 f(.) = 0.000108 \n",
      "iter = 843 ||∇f(.)|| = 0.0050 f(.) = 0.000107 \n",
      "iter = 844 ||∇f(.)|| = 0.0050 f(.) = 0.000107 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 845 ||∇f(.)|| = 0.0050 f(.) = 0.000107 \n",
      "iter = 846 ||∇f(.)|| = 0.0050 f(.) = 0.000107 \n",
      "iter = 847 ||∇f(.)|| = 0.0050 f(.) = 0.000106 \n",
      "iter = 848 ||∇f(.)|| = 0.0050 f(.) = 0.000106 \n",
      "iter = 849 ||∇f(.)|| = 0.0050 f(.) = 0.000106 \n",
      "iter = 850 ||∇f(.)|| = 0.0050 f(.) = 0.000106 \n",
      "iter = 851 ||∇f(.)|| = 0.0049 f(.) = 0.000105 \n",
      "iter = 852 ||∇f(.)|| = 0.0049 f(.) = 0.000105 \n",
      "iter = 853 ||∇f(.)|| = 0.0049 f(.) = 0.000105 \n",
      "iter = 854 ||∇f(.)|| = 0.0049 f(.) = 0.000105 \n",
      "iter = 855 ||∇f(.)|| = 0.0049 f(.) = 0.000104 \n",
      "iter = 856 ||∇f(.)|| = 0.0049 f(.) = 0.000104 \n",
      "iter = 857 ||∇f(.)|| = 0.0049 f(.) = 0.000104 \n",
      "iter = 858 ||∇f(.)|| = 0.0049 f(.) = 0.000104 \n",
      "iter = 859 ||∇f(.)|| = 0.0049 f(.) = 0.000103 \n",
      "iter = 860 ||∇f(.)|| = 0.0049 f(.) = 0.000103 \n",
      "iter = 861 ||∇f(.)|| = 0.0049 f(.) = 0.000103 \n",
      "iter = 862 ||∇f(.)|| = 0.0049 f(.) = 0.000103 \n",
      "iter = 863 ||∇f(.)|| = 0.0048 f(.) = 0.000103 \n",
      "iter = 864 ||∇f(.)|| = 0.0048 f(.) = 0.000102 \n",
      "iter = 865 ||∇f(.)|| = 0.0048 f(.) = 0.000102 \n",
      "iter = 866 ||∇f(.)|| = 0.0048 f(.) = 0.000102 \n",
      "iter = 867 ||∇f(.)|| = 0.0048 f(.) = 0.000102 \n",
      "iter = 868 ||∇f(.)|| = 0.0048 f(.) = 0.000101 \n",
      "iter = 869 ||∇f(.)|| = 0.0048 f(.) = 0.000101 \n",
      "iter = 870 ||∇f(.)|| = 0.0048 f(.) = 0.000101 \n",
      "iter = 871 ||∇f(.)|| = 0.0048 f(.) = 0.000101 \n",
      "iter = 872 ||∇f(.)|| = 0.0048 f(.) = 0.000100 \n",
      "iter = 873 ||∇f(.)|| = 0.0048 f(.) = 0.000100 \n",
      "iter = 874 ||∇f(.)|| = 0.0048 f(.) = 0.000100 \n",
      "iter = 875 ||∇f(.)|| = 0.0047 f(.) = 0.000100 \n",
      "iter = 876 ||∇f(.)|| = 0.0047 f(.) = 0.000100 \n",
      "iter = 877 ||∇f(.)|| = 0.0047 f(.) = 0.000099 \n",
      "iter = 878 ||∇f(.)|| = 0.0047 f(.) = 0.000099 \n",
      "iter = 879 ||∇f(.)|| = 0.0047 f(.) = 0.000099 \n",
      "iter = 880 ||∇f(.)|| = 0.0047 f(.) = 0.000099 \n",
      "iter = 881 ||∇f(.)|| = 0.0047 f(.) = 0.000098 \n",
      "iter = 882 ||∇f(.)|| = 0.0047 f(.) = 0.000098 \n",
      "iter = 883 ||∇f(.)|| = 0.0047 f(.) = 0.000098 \n",
      "iter = 884 ||∇f(.)|| = 0.0047 f(.) = 0.000098 \n",
      "iter = 885 ||∇f(.)|| = 0.0047 f(.) = 0.000098 \n",
      "iter = 886 ||∇f(.)|| = 0.0047 f(.) = 0.000097 \n",
      "iter = 887 ||∇f(.)|| = 0.0047 f(.) = 0.000097 \n",
      "iter = 888 ||∇f(.)|| = 0.0046 f(.) = 0.000097 \n",
      "iter = 889 ||∇f(.)|| = 0.0046 f(.) = 0.000097 \n",
      "iter = 890 ||∇f(.)|| = 0.0046 f(.) = 0.000096 \n",
      "iter = 891 ||∇f(.)|| = 0.0046 f(.) = 0.000096 \n",
      "iter = 892 ||∇f(.)|| = 0.0046 f(.) = 0.000096 \n",
      "iter = 893 ||∇f(.)|| = 0.0046 f(.) = 0.000096 \n",
      "iter = 894 ||∇f(.)|| = 0.0046 f(.) = 0.000096 \n",
      "iter = 895 ||∇f(.)|| = 0.0046 f(.) = 0.000095 \n",
      "iter = 896 ||∇f(.)|| = 0.0046 f(.) = 0.000095 \n",
      "iter = 897 ||∇f(.)|| = 0.0046 f(.) = 0.000095 \n",
      "iter = 898 ||∇f(.)|| = 0.0046 f(.) = 0.000095 \n",
      "iter = 899 ||∇f(.)|| = 0.0046 f(.) = 0.000095 \n",
      "iter = 900 ||∇f(.)|| = 0.0046 f(.) = 0.000094 \n",
      "iter = 901 ||∇f(.)|| = 0.0045 f(.) = 0.000094 \n",
      "iter = 902 ||∇f(.)|| = 0.0045 f(.) = 0.000094 \n",
      "iter = 903 ||∇f(.)|| = 0.0045 f(.) = 0.000094 \n",
      "iter = 904 ||∇f(.)|| = 0.0045 f(.) = 0.000094 \n",
      "iter = 905 ||∇f(.)|| = 0.0045 f(.) = 0.000093 \n",
      "iter = 906 ||∇f(.)|| = 0.0045 f(.) = 0.000093 \n",
      "iter = 907 ||∇f(.)|| = 0.0045 f(.) = 0.000093 \n",
      "iter = 908 ||∇f(.)|| = 0.0045 f(.) = 0.000093 \n",
      "iter = 909 ||∇f(.)|| = 0.0045 f(.) = 0.000092 \n",
      "iter = 910 ||∇f(.)|| = 0.0045 f(.) = 0.000092 \n",
      "iter = 911 ||∇f(.)|| = 0.0045 f(.) = 0.000092 \n",
      "iter = 912 ||∇f(.)|| = 0.0045 f(.) = 0.000092 \n",
      "iter = 913 ||∇f(.)|| = 0.0045 f(.) = 0.000092 \n",
      "iter = 914 ||∇f(.)|| = 0.0045 f(.) = 0.000091 \n",
      "iter = 915 ||∇f(.)|| = 0.0044 f(.) = 0.000091 \n",
      "iter = 916 ||∇f(.)|| = 0.0044 f(.) = 0.000091 \n",
      "iter = 917 ||∇f(.)|| = 0.0044 f(.) = 0.000091 \n",
      "iter = 918 ||∇f(.)|| = 0.0044 f(.) = 0.000091 \n",
      "iter = 919 ||∇f(.)|| = 0.0044 f(.) = 0.000091 \n",
      "iter = 920 ||∇f(.)|| = 0.0044 f(.) = 0.000090 \n",
      "iter = 921 ||∇f(.)|| = 0.0044 f(.) = 0.000090 \n",
      "iter = 922 ||∇f(.)|| = 0.0044 f(.) = 0.000090 \n",
      "iter = 923 ||∇f(.)|| = 0.0044 f(.) = 0.000090 \n",
      "iter = 924 ||∇f(.)|| = 0.0044 f(.) = 0.000090 \n",
      "iter = 925 ||∇f(.)|| = 0.0044 f(.) = 0.000089 \n",
      "iter = 926 ||∇f(.)|| = 0.0044 f(.) = 0.000089 \n",
      "iter = 927 ||∇f(.)|| = 0.0044 f(.) = 0.000089 \n",
      "iter = 928 ||∇f(.)|| = 0.0044 f(.) = 0.000089 \n",
      "iter = 929 ||∇f(.)|| = 0.0043 f(.) = 0.000089 \n",
      "iter = 930 ||∇f(.)|| = 0.0043 f(.) = 0.000088 \n",
      "iter = 931 ||∇f(.)|| = 0.0043 f(.) = 0.000088 \n",
      "iter = 932 ||∇f(.)|| = 0.0043 f(.) = 0.000088 \n",
      "iter = 933 ||∇f(.)|| = 0.0043 f(.) = 0.000088 \n",
      "iter = 934 ||∇f(.)|| = 0.0043 f(.) = 0.000088 \n",
      "iter = 935 ||∇f(.)|| = 0.0043 f(.) = 0.000087 \n",
      "iter = 936 ||∇f(.)|| = 0.0043 f(.) = 0.000087 \n",
      "iter = 937 ||∇f(.)|| = 0.0043 f(.) = 0.000087 \n",
      "iter = 938 ||∇f(.)|| = 0.0043 f(.) = 0.000087 \n",
      "iter = 939 ||∇f(.)|| = 0.0043 f(.) = 0.000087 \n",
      "iter = 940 ||∇f(.)|| = 0.0043 f(.) = 0.000087 \n",
      "iter = 941 ||∇f(.)|| = 0.0043 f(.) = 0.000086 \n",
      "iter = 942 ||∇f(.)|| = 0.0043 f(.) = 0.000086 \n",
      "iter = 943 ||∇f(.)|| = 0.0042 f(.) = 0.000086 \n",
      "iter = 944 ||∇f(.)|| = 0.0042 f(.) = 0.000086 \n",
      "iter = 945 ||∇f(.)|| = 0.0042 f(.) = 0.000086 \n",
      "iter = 946 ||∇f(.)|| = 0.0042 f(.) = 0.000085 \n",
      "iter = 947 ||∇f(.)|| = 0.0042 f(.) = 0.000085 \n",
      "iter = 948 ||∇f(.)|| = 0.0042 f(.) = 0.000085 \n",
      "iter = 949 ||∇f(.)|| = 0.0042 f(.) = 0.000085 \n",
      "iter = 950 ||∇f(.)|| = 0.0042 f(.) = 0.000085 \n",
      "iter = 951 ||∇f(.)|| = 0.0042 f(.) = 0.000085 \n",
      "iter = 952 ||∇f(.)|| = 0.0042 f(.) = 0.000084 \n",
      "iter = 953 ||∇f(.)|| = 0.0042 f(.) = 0.000084 \n",
      "iter = 954 ||∇f(.)|| = 0.0042 f(.) = 0.000084 \n",
      "iter = 955 ||∇f(.)|| = 0.0042 f(.) = 0.000084 \n",
      "iter = 956 ||∇f(.)|| = 0.0042 f(.) = 0.000084 \n",
      "iter = 957 ||∇f(.)|| = 0.0042 f(.) = 0.000084 \n",
      "iter = 958 ||∇f(.)|| = 0.0041 f(.) = 0.000083 \n",
      "iter = 959 ||∇f(.)|| = 0.0041 f(.) = 0.000083 \n",
      "iter = 960 ||∇f(.)|| = 0.0041 f(.) = 0.000083 \n",
      "iter = 961 ||∇f(.)|| = 0.0041 f(.) = 0.000083 \n",
      "iter = 962 ||∇f(.)|| = 0.0041 f(.) = 0.000083 \n",
      "iter = 963 ||∇f(.)|| = 0.0041 f(.) = 0.000083 \n",
      "iter = 964 ||∇f(.)|| = 0.0041 f(.) = 0.000082 \n",
      "iter = 965 ||∇f(.)|| = 0.0041 f(.) = 0.000082 \n",
      "iter = 966 ||∇f(.)|| = 0.0041 f(.) = 0.000082 \n",
      "iter = 967 ||∇f(.)|| = 0.0041 f(.) = 0.000082 \n",
      "iter = 968 ||∇f(.)|| = 0.0041 f(.) = 0.000082 \n",
      "iter = 969 ||∇f(.)|| = 0.0041 f(.) = 0.000081 \n",
      "iter = 970 ||∇f(.)|| = 0.0041 f(.) = 0.000081 \n",
      "iter = 971 ||∇f(.)|| = 0.0041 f(.) = 0.000081 \n",
      "iter = 972 ||∇f(.)|| = 0.0041 f(.) = 0.000081 \n",
      "iter = 973 ||∇f(.)|| = 0.0041 f(.) = 0.000081 \n",
      "iter = 974 ||∇f(.)|| = 0.0040 f(.) = 0.000081 \n",
      "iter = 975 ||∇f(.)|| = 0.0040 f(.) = 0.000081 \n",
      "iter = 976 ||∇f(.)|| = 0.0040 f(.) = 0.000080 \n",
      "iter = 977 ||∇f(.)|| = 0.0040 f(.) = 0.000080 \n",
      "iter = 978 ||∇f(.)|| = 0.0040 f(.) = 0.000080 \n",
      "iter = 979 ||∇f(.)|| = 0.0040 f(.) = 0.000080 \n",
      "iter = 980 ||∇f(.)|| = 0.0040 f(.) = 0.000080 \n",
      "iter = 981 ||∇f(.)|| = 0.0040 f(.) = 0.000080 \n",
      "iter = 982 ||∇f(.)|| = 0.0040 f(.) = 0.000079 \n",
      "iter = 983 ||∇f(.)|| = 0.0040 f(.) = 0.000079 \n",
      "iter = 984 ||∇f(.)|| = 0.0040 f(.) = 0.000079 \n",
      "iter = 985 ||∇f(.)|| = 0.0040 f(.) = 0.000079 \n",
      "iter = 986 ||∇f(.)|| = 0.0040 f(.) = 0.000079 \n",
      "iter = 987 ||∇f(.)|| = 0.0040 f(.) = 0.000079 \n",
      "iter = 988 ||∇f(.)|| = 0.0040 f(.) = 0.000078 \n",
      "iter = 989 ||∇f(.)|| = 0.0040 f(.) = 0.000078 \n",
      "iter = 990 ||∇f(.)|| = 0.0040 f(.) = 0.000078 \n",
      "iter = 991 ||∇f(.)|| = 0.0039 f(.) = 0.000078 \n",
      "iter = 992 ||∇f(.)|| = 0.0039 f(.) = 0.000078 \n",
      "iter = 993 ||∇f(.)|| = 0.0039 f(.) = 0.000078 \n",
      "iter = 994 ||∇f(.)|| = 0.0039 f(.) = 0.000077 \n",
      "iter = 995 ||∇f(.)|| = 0.0039 f(.) = 0.000077 \n",
      "iter = 996 ||∇f(.)|| = 0.0039 f(.) = 0.000077 \n",
      "iter = 997 ||∇f(.)|| = 0.0039 f(.) = 0.000077 \n",
      "iter = 998 ||∇f(.)|| = 0.0039 f(.) = 0.000077 \n",
      "iter = 999 ||∇f(.)|| = 0.0039 f(.) = 0.000077 \n",
      "iter = 1000 ||∇f(.)|| = 0.0039 f(.) = 0.000077 \n",
      "iter = 1001 ||∇f(.)|| = 0.0039 f(.) = 0.000076 \n",
      "iter = 1002 ||∇f(.)|| = 0.0039 f(.) = 0.000076 \n",
      "iter = 1003 ||∇f(.)|| = 0.0039 f(.) = 0.000076 \n",
      "iter = 1004 ||∇f(.)|| = 0.0039 f(.) = 0.000076 \n",
      "iter = 1005 ||∇f(.)|| = 0.0039 f(.) = 0.000076 \n",
      "iter = 1006 ||∇f(.)|| = 0.0039 f(.) = 0.000076 \n",
      "iter = 1007 ||∇f(.)|| = 0.0039 f(.) = 0.000076 \n",
      "iter = 1008 ||∇f(.)|| = 0.0038 f(.) = 0.000075 \n",
      "iter = 1009 ||∇f(.)|| = 0.0038 f(.) = 0.000075 \n",
      "iter = 1010 ||∇f(.)|| = 0.0038 f(.) = 0.000075 \n",
      "iter = 1011 ||∇f(.)|| = 0.0038 f(.) = 0.000075 \n",
      "iter = 1012 ||∇f(.)|| = 0.0038 f(.) = 0.000075 \n",
      "iter = 1013 ||∇f(.)|| = 0.0038 f(.) = 0.000075 \n",
      "iter = 1014 ||∇f(.)|| = 0.0038 f(.) = 0.000074 \n",
      "iter = 1015 ||∇f(.)|| = 0.0038 f(.) = 0.000074 \n",
      "iter = 1016 ||∇f(.)|| = 0.0038 f(.) = 0.000074 \n",
      "iter = 1017 ||∇f(.)|| = 0.0038 f(.) = 0.000074 \n",
      "iter = 1018 ||∇f(.)|| = 0.0038 f(.) = 0.000074 \n",
      "iter = 1019 ||∇f(.)|| = 0.0038 f(.) = 0.000074 \n",
      "iter = 1020 ||∇f(.)|| = 0.0038 f(.) = 0.000074 \n",
      "iter = 1021 ||∇f(.)|| = 0.0038 f(.) = 0.000073 \n",
      "iter = 1022 ||∇f(.)|| = 0.0038 f(.) = 0.000073 \n",
      "iter = 1023 ||∇f(.)|| = 0.0038 f(.) = 0.000073 \n",
      "iter = 1024 ||∇f(.)|| = 0.0038 f(.) = 0.000073 \n",
      "iter = 1025 ||∇f(.)|| = 0.0038 f(.) = 0.000073 \n",
      "iter = 1026 ||∇f(.)|| = 0.0037 f(.) = 0.000073 \n",
      "iter = 1027 ||∇f(.)|| = 0.0037 f(.) = 0.000073 \n",
      "iter = 1028 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1029 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1030 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1031 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1032 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1033 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1034 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1035 ||∇f(.)|| = 0.0037 f(.) = 0.000072 \n",
      "iter = 1036 ||∇f(.)|| = 0.0037 f(.) = 0.000071 \n",
      "iter = 1037 ||∇f(.)|| = 0.0037 f(.) = 0.000071 \n",
      "iter = 1038 ||∇f(.)|| = 0.0037 f(.) = 0.000071 \n",
      "iter = 1039 ||∇f(.)|| = 0.0037 f(.) = 0.000071 \n",
      "iter = 1040 ||∇f(.)|| = 0.0037 f(.) = 0.000071 \n",
      "iter = 1041 ||∇f(.)|| = 0.0037 f(.) = 0.000071 \n",
      "iter = 1042 ||∇f(.)|| = 0.0037 f(.) = 0.000071 \n",
      "iter = 1043 ||∇f(.)|| = 0.0037 f(.) = 0.000070 \n",
      "iter = 1044 ||∇f(.)|| = 0.0037 f(.) = 0.000070 \n",
      "iter = 1045 ||∇f(.)|| = 0.0036 f(.) = 0.000070 \n",
      "iter = 1046 ||∇f(.)|| = 0.0036 f(.) = 0.000070 \n",
      "iter = 1047 ||∇f(.)|| = 0.0036 f(.) = 0.000070 \n",
      "iter = 1048 ||∇f(.)|| = 0.0036 f(.) = 0.000070 \n",
      "iter = 1049 ||∇f(.)|| = 0.0036 f(.) = 0.000070 \n",
      "iter = 1050 ||∇f(.)|| = 0.0036 f(.) = 0.000070 \n",
      "iter = 1051 ||∇f(.)|| = 0.0036 f(.) = 0.000069 \n",
      "iter = 1052 ||∇f(.)|| = 0.0036 f(.) = 0.000069 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 1053 ||∇f(.)|| = 0.0036 f(.) = 0.000069 \n",
      "iter = 1054 ||∇f(.)|| = 0.0036 f(.) = 0.000069 \n",
      "iter = 1055 ||∇f(.)|| = 0.0036 f(.) = 0.000069 \n",
      "iter = 1056 ||∇f(.)|| = 0.0036 f(.) = 0.000069 \n",
      "iter = 1057 ||∇f(.)|| = 0.0036 f(.) = 0.000069 \n",
      "iter = 1058 ||∇f(.)|| = 0.0036 f(.) = 0.000068 \n",
      "iter = 1059 ||∇f(.)|| = 0.0036 f(.) = 0.000068 \n",
      "iter = 1060 ||∇f(.)|| = 0.0036 f(.) = 0.000068 \n",
      "iter = 1061 ||∇f(.)|| = 0.0036 f(.) = 0.000068 \n",
      "iter = 1062 ||∇f(.)|| = 0.0036 f(.) = 0.000068 \n",
      "iter = 1063 ||∇f(.)|| = 0.0036 f(.) = 0.000068 \n",
      "iter = 1064 ||∇f(.)|| = 0.0036 f(.) = 0.000068 \n",
      "iter = 1065 ||∇f(.)|| = 0.0035 f(.) = 0.000068 \n",
      "iter = 1066 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1067 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1068 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1069 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1070 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1071 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1072 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1073 ||∇f(.)|| = 0.0035 f(.) = 0.000067 \n",
      "iter = 1074 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1075 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1076 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1077 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1078 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1079 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1080 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1081 ||∇f(.)|| = 0.0035 f(.) = 0.000066 \n",
      "iter = 1082 ||∇f(.)|| = 0.0035 f(.) = 0.000065 \n",
      "iter = 1083 ||∇f(.)|| = 0.0035 f(.) = 0.000065 \n",
      "iter = 1084 ||∇f(.)|| = 0.0035 f(.) = 0.000065 \n",
      "iter = 1085 ||∇f(.)|| = 0.0034 f(.) = 0.000065 \n",
      "iter = 1086 ||∇f(.)|| = 0.0034 f(.) = 0.000065 \n",
      "iter = 1087 ||∇f(.)|| = 0.0034 f(.) = 0.000065 \n",
      "iter = 1088 ||∇f(.)|| = 0.0034 f(.) = 0.000065 \n",
      "iter = 1089 ||∇f(.)|| = 0.0034 f(.) = 0.000065 \n",
      "iter = 1090 ||∇f(.)|| = 0.0034 f(.) = 0.000065 \n",
      "iter = 1091 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1092 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1093 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1094 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1095 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1096 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1097 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1098 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1099 ||∇f(.)|| = 0.0034 f(.) = 0.000064 \n",
      "iter = 1100 ||∇f(.)|| = 0.0034 f(.) = 0.000063 \n",
      "iter = 1101 ||∇f(.)|| = 0.0034 f(.) = 0.000063 \n",
      "iter = 1102 ||∇f(.)|| = 0.0034 f(.) = 0.000063 \n",
      "iter = 1103 ||∇f(.)|| = 0.0034 f(.) = 0.000063 \n",
      "iter = 1104 ||∇f(.)|| = 0.0034 f(.) = 0.000063 \n",
      "iter = 1105 ||∇f(.)|| = 0.0034 f(.) = 0.000063 \n",
      "iter = 1106 ||∇f(.)|| = 0.0034 f(.) = 0.000063 \n",
      "iter = 1107 ||∇f(.)|| = 0.0033 f(.) = 0.000063 \n",
      "iter = 1108 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1109 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1110 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1111 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1112 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1113 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1114 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1115 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1116 ||∇f(.)|| = 0.0033 f(.) = 0.000062 \n",
      "iter = 1117 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1118 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1119 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1120 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1121 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1122 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1123 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1124 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1125 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1126 ||∇f(.)|| = 0.0033 f(.) = 0.000061 \n",
      "iter = 1127 ||∇f(.)|| = 0.0033 f(.) = 0.000060 \n",
      "iter = 1128 ||∇f(.)|| = 0.0033 f(.) = 0.000060 \n",
      "iter = 1129 ||∇f(.)|| = 0.0033 f(.) = 0.000060 \n",
      "iter = 1130 ||∇f(.)|| = 0.0032 f(.) = 0.000060 \n",
      "iter = 1131 ||∇f(.)|| = 0.0032 f(.) = 0.000060 \n",
      "iter = 1132 ||∇f(.)|| = 0.0032 f(.) = 0.000060 \n",
      "iter = 1133 ||∇f(.)|| = 0.0032 f(.) = 0.000060 \n",
      "iter = 1134 ||∇f(.)|| = 0.0032 f(.) = 0.000060 \n",
      "iter = 1135 ||∇f(.)|| = 0.0032 f(.) = 0.000060 \n",
      "iter = 1136 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1137 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1138 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1139 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1140 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1141 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1142 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1143 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1144 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1145 ||∇f(.)|| = 0.0032 f(.) = 0.000059 \n",
      "iter = 1146 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1147 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1148 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1149 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1150 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1151 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1152 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1153 ||∇f(.)|| = 0.0032 f(.) = 0.000058 \n",
      "iter = 1154 ||∇f(.)|| = 0.0031 f(.) = 0.000058 \n",
      "iter = 1155 ||∇f(.)|| = 0.0031 f(.) = 0.000058 \n",
      "iter = 1156 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1157 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1158 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1159 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1160 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1161 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1162 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1163 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1164 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1165 ||∇f(.)|| = 0.0031 f(.) = 0.000057 \n",
      "iter = 1166 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1167 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1168 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1169 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1170 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1171 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1172 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1173 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1174 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1175 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1176 ||∇f(.)|| = 0.0031 f(.) = 0.000056 \n",
      "iter = 1177 ||∇f(.)|| = 0.0031 f(.) = 0.000055 \n",
      "iter = 1178 ||∇f(.)|| = 0.0031 f(.) = 0.000055 \n",
      "iter = 1179 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1180 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1181 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1182 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1183 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1184 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1185 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1186 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1187 ||∇f(.)|| = 0.0030 f(.) = 0.000055 \n",
      "iter = 1188 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1189 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1190 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1191 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1192 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1193 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1194 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1195 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1196 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1197 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1198 ||∇f(.)|| = 0.0030 f(.) = 0.000054 \n",
      "iter = 1199 ||∇f(.)|| = 0.0030 f(.) = 0.000053 \n",
      "iter = 1200 ||∇f(.)|| = 0.0030 f(.) = 0.000053 \n",
      "iter = 1201 ||∇f(.)|| = 0.0030 f(.) = 0.000053 \n",
      "iter = 1202 ||∇f(.)|| = 0.0030 f(.) = 0.000053 \n",
      "iter = 1203 ||∇f(.)|| = 0.0030 f(.) = 0.000053 \n",
      "iter = 1204 ||∇f(.)|| = 0.0030 f(.) = 0.000053 \n",
      "iter = 1205 ||∇f(.)|| = 0.0030 f(.) = 0.000053 \n",
      "iter = 1206 ||∇f(.)|| = 0.0029 f(.) = 0.000053 \n",
      "iter = 1207 ||∇f(.)|| = 0.0029 f(.) = 0.000053 \n",
      "iter = 1208 ||∇f(.)|| = 0.0029 f(.) = 0.000053 \n",
      "iter = 1209 ||∇f(.)|| = 0.0029 f(.) = 0.000053 \n",
      "iter = 1210 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1211 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1212 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1213 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1214 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1215 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1216 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1217 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1218 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1219 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1220 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1221 ||∇f(.)|| = 0.0029 f(.) = 0.000052 \n",
      "iter = 1222 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1223 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1224 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1225 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1226 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1227 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1228 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1229 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1230 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1231 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1232 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1233 ||∇f(.)|| = 0.0029 f(.) = 0.000051 \n",
      "iter = 1234 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1235 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1236 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1237 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1238 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1239 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1240 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1241 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1242 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1243 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1244 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1245 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1246 ||∇f(.)|| = 0.0028 f(.) = 0.000050 \n",
      "iter = 1247 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1248 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1249 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1250 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1251 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1252 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1253 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1254 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1255 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1256 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1257 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 1258 ||∇f(.)|| = 0.0028 f(.) = 0.000049 \n",
      "iter = 1259 ||∇f(.)|| = 0.0028 f(.) = 0.000048 \n",
      "iter = 1260 ||∇f(.)|| = 0.0028 f(.) = 0.000048 \n",
      "iter = 1261 ||∇f(.)|| = 0.0028 f(.) = 0.000048 \n",
      "iter = 1262 ||∇f(.)|| = 0.0028 f(.) = 0.000048 \n",
      "iter = 1263 ||∇f(.)|| = 0.0028 f(.) = 0.000048 \n",
      "iter = 1264 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1265 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1266 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1267 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1268 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1269 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1270 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1271 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1272 ||∇f(.)|| = 0.0027 f(.) = 0.000048 \n",
      "iter = 1273 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1274 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1275 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1276 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1277 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1278 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1279 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1280 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1281 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1282 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1283 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1284 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1285 ||∇f(.)|| = 0.0027 f(.) = 0.000047 \n",
      "iter = 1286 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1287 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1288 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1289 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1290 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1291 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1292 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1293 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1294 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1295 ||∇f(.)|| = 0.0027 f(.) = 0.000046 \n",
      "iter = 1296 ||∇f(.)|| = 0.0026 f(.) = 0.000046 \n",
      "iter = 1297 ||∇f(.)|| = 0.0026 f(.) = 0.000046 \n",
      "iter = 1298 ||∇f(.)|| = 0.0026 f(.) = 0.000046 \n",
      "iter = 1299 ||∇f(.)|| = 0.0026 f(.) = 0.000046 \n",
      "iter = 1300 ||∇f(.)|| = 0.0026 f(.) = 0.000046 \n",
      "iter = 1301 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1302 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1303 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1304 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1305 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1306 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1307 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1308 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1309 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1310 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1311 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1312 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1313 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1314 ||∇f(.)|| = 0.0026 f(.) = 0.000045 \n",
      "iter = 1315 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1316 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1317 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1318 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1319 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1320 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1321 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1322 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1323 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1324 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1325 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1326 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1327 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1328 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1329 ||∇f(.)|| = 0.0026 f(.) = 0.000044 \n",
      "iter = 1330 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1331 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1332 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1333 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1334 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1335 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1336 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1337 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1338 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1339 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1340 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1341 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1342 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1343 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1344 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1345 ||∇f(.)|| = 0.0025 f(.) = 0.000043 \n",
      "iter = 1346 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1347 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1348 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1349 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1350 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1351 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1352 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1353 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1354 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1355 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1356 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1357 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1358 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1359 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1360 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1361 ||∇f(.)|| = 0.0025 f(.) = 0.000042 \n",
      "iter = 1362 ||∇f(.)|| = 0.0025 f(.) = 0.000041 \n",
      "iter = 1363 ||∇f(.)|| = 0.0025 f(.) = 0.000041 \n",
      "iter = 1364 ||∇f(.)|| = 0.0025 f(.) = 0.000041 \n",
      "iter = 1365 ||∇f(.)|| = 0.0025 f(.) = 0.000041 \n",
      "iter = 1366 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1367 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1368 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1369 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1370 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1371 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1372 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1373 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1374 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1375 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1376 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1377 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1378 ||∇f(.)|| = 0.0024 f(.) = 0.000041 \n",
      "iter = 1379 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1380 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1381 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1382 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1383 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1384 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1385 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1386 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1387 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1388 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1389 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1390 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1391 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1392 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1393 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1394 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1395 ||∇f(.)|| = 0.0024 f(.) = 0.000040 \n",
      "iter = 1396 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1397 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1398 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1399 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1400 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1401 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1402 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1403 ||∇f(.)|| = 0.0024 f(.) = 0.000039 \n",
      "iter = 1404 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1405 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1406 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1407 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1408 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1409 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1410 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1411 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1412 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1413 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1414 ||∇f(.)|| = 0.0023 f(.) = 0.000039 \n",
      "iter = 1415 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1416 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1417 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1418 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1419 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1420 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1421 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1422 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1423 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1424 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1425 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1426 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1427 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1428 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1429 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1430 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1431 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1432 ||∇f(.)|| = 0.0023 f(.) = 0.000038 \n",
      "iter = 1433 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1434 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1435 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1436 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1437 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1438 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1439 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1440 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1441 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1442 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1443 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1444 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1445 ||∇f(.)|| = 0.0023 f(.) = 0.000037 \n",
      "iter = 1446 ||∇f(.)|| = 0.0022 f(.) = 0.000037 \n",
      "iter = 1447 ||∇f(.)|| = 0.0022 f(.) = 0.000037 \n",
      "iter = 1448 ||∇f(.)|| = 0.0022 f(.) = 0.000037 \n",
      "iter = 1449 ||∇f(.)|| = 0.0022 f(.) = 0.000037 \n",
      "iter = 1450 ||∇f(.)|| = 0.0022 f(.) = 0.000037 \n",
      "iter = 1451 ||∇f(.)|| = 0.0022 f(.) = 0.000037 \n",
      "iter = 1452 ||∇f(.)|| = 0.0022 f(.) = 0.000037 \n",
      "iter = 1453 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1454 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1455 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1456 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1457 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1458 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1459 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1460 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1461 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1462 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1463 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1464 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1465 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1466 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1467 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1468 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1469 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1470 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1471 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1472 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1473 ||∇f(.)|| = 0.0022 f(.) = 0.000036 \n",
      "iter = 1474 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1475 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1476 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1477 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1478 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1479 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1480 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1481 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1482 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1483 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1484 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 1485 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1486 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1487 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1488 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1489 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1490 ||∇f(.)|| = 0.0022 f(.) = 0.000035 \n",
      "iter = 1491 ||∇f(.)|| = 0.0021 f(.) = 0.000035 \n",
      "iter = 1492 ||∇f(.)|| = 0.0021 f(.) = 0.000035 \n",
      "iter = 1493 ||∇f(.)|| = 0.0021 f(.) = 0.000035 \n",
      "iter = 1494 ||∇f(.)|| = 0.0021 f(.) = 0.000035 \n",
      "iter = 1495 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1496 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1497 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1498 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1499 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1500 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1501 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1502 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1503 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1504 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1505 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1506 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1507 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1508 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1509 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1510 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1511 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1512 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1513 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1514 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1515 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1516 ||∇f(.)|| = 0.0021 f(.) = 0.000034 \n",
      "iter = 1517 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1518 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1519 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1520 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1521 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1522 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1523 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1524 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1525 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1526 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1527 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1528 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1529 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1530 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1531 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1532 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1533 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1534 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1535 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1536 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1537 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1538 ||∇f(.)|| = 0.0021 f(.) = 0.000033 \n",
      "iter = 1539 ||∇f(.)|| = 0.0020 f(.) = 0.000033 \n",
      "iter = 1540 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1541 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1542 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1543 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1544 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1545 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1546 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1547 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1548 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1549 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1550 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1551 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1552 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1553 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1554 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1555 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1556 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1557 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1558 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1559 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1560 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1561 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1562 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1563 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1564 ||∇f(.)|| = 0.0020 f(.) = 0.000032 \n",
      "iter = 1565 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1566 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1567 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1568 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1569 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1570 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1571 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1572 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1573 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1574 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1575 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1576 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1577 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1578 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1579 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1580 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1581 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1582 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1583 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1584 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1585 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1586 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1587 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1588 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1589 ||∇f(.)|| = 0.0020 f(.) = 0.000031 \n",
      "iter = 1590 ||∇f(.)|| = 0.0020 f(.) = 0.000030 \n",
      "iter = 1591 ||∇f(.)|| = 0.0020 f(.) = 0.000030 \n",
      "iter = 1592 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1593 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1594 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1595 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1596 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1597 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1598 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1599 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1600 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1601 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1602 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1603 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1604 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1605 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1606 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1607 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1608 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1609 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1610 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1611 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1612 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1613 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1614 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1615 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1616 ||∇f(.)|| = 0.0019 f(.) = 0.000030 \n",
      "iter = 1617 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1618 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1619 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1620 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1621 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1622 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1623 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1624 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1625 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1626 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1627 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1628 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1629 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1630 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1631 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1632 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1633 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1634 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1635 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1636 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1637 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1638 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1639 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1640 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1641 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1642 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1643 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1644 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1645 ||∇f(.)|| = 0.0019 f(.) = 0.000029 \n",
      "iter = 1646 ||∇f(.)|| = 0.0019 f(.) = 0.000028 \n",
      "iter = 1647 ||∇f(.)|| = 0.0019 f(.) = 0.000028 \n",
      "iter = 1648 ||∇f(.)|| = 0.0019 f(.) = 0.000028 \n",
      "iter = 1649 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1650 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1651 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1652 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1653 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1654 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1655 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1656 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1657 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1658 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1659 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1660 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1661 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1662 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1663 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1664 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1665 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1666 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1667 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1668 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1669 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1670 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1671 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1672 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1673 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1674 ||∇f(.)|| = 0.0018 f(.) = 0.000028 \n",
      "iter = 1675 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1676 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1677 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1678 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1679 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1680 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1681 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1682 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1683 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1684 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1685 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1686 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1687 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1688 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1689 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 1690 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1691 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1692 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1693 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1694 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1695 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1696 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1697 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1698 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1699 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1700 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1701 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1702 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1703 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1704 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1705 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1706 ||∇f(.)|| = 0.0018 f(.) = 0.000027 \n",
      "iter = 1707 ||∇f(.)|| = 0.0018 f(.) = 0.000026 \n",
      "iter = 1708 ||∇f(.)|| = 0.0018 f(.) = 0.000026 \n",
      "iter = 1709 ||∇f(.)|| = 0.0018 f(.) = 0.000026 \n",
      "iter = 1710 ||∇f(.)|| = 0.0018 f(.) = 0.000026 \n",
      "iter = 1711 ||∇f(.)|| = 0.0018 f(.) = 0.000026 \n",
      "iter = 1712 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1713 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1714 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1715 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1716 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1717 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1718 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1719 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1720 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1721 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1722 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1723 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1724 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1725 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1726 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1727 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1728 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1729 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1730 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1731 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1732 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1733 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1734 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1735 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1736 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1737 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1738 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1739 ||∇f(.)|| = 0.0017 f(.) = 0.000026 \n",
      "iter = 1740 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1741 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1742 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1743 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1744 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1745 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1746 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1747 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1748 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1749 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1750 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1751 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1752 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1753 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1754 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1755 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1756 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1757 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1758 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1759 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1760 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1761 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1762 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1763 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1764 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1765 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1766 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1767 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1768 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1769 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1770 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1771 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1772 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1773 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1774 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1775 ||∇f(.)|| = 0.0017 f(.) = 0.000025 \n",
      "iter = 1776 ||∇f(.)|| = 0.0017 f(.) = 0.000024 \n",
      "iter = 1777 ||∇f(.)|| = 0.0017 f(.) = 0.000024 \n",
      "iter = 1778 ||∇f(.)|| = 0.0017 f(.) = 0.000024 \n",
      "iter = 1779 ||∇f(.)|| = 0.0017 f(.) = 0.000024 \n",
      "iter = 1780 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1781 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1782 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1783 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1784 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1785 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1786 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1787 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1788 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1789 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1790 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1791 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1792 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1793 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1794 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1795 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1796 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1797 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1798 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1799 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1800 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1801 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1802 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1803 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1804 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1805 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1806 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1807 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1808 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1809 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1810 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1811 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1812 ||∇f(.)|| = 0.0016 f(.) = 0.000024 \n",
      "iter = 1813 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1814 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1815 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1816 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1817 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1818 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1819 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1820 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1821 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1822 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1823 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1824 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1825 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1826 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1827 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1828 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1829 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1830 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1831 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1832 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1833 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1834 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1835 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1836 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1837 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1838 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1839 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1840 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1841 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1842 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1843 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1844 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1845 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1846 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1847 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1848 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1849 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1850 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1851 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1852 ||∇f(.)|| = 0.0016 f(.) = 0.000023 \n",
      "iter = 1853 ||∇f(.)|| = 0.0016 f(.) = 0.000022 \n",
      "iter = 1854 ||∇f(.)|| = 0.0016 f(.) = 0.000022 \n",
      "iter = 1855 ||∇f(.)|| = 0.0016 f(.) = 0.000022 \n",
      "iter = 1856 ||∇f(.)|| = 0.0016 f(.) = 0.000022 \n",
      "iter = 1857 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1858 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1859 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1860 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1861 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1862 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1863 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1864 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1865 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1866 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1867 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1868 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1869 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1870 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1871 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1872 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1873 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1874 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1875 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1876 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1877 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1878 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1879 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1880 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1881 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1882 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1883 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1884 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1885 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1886 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1887 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1888 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1889 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1890 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1891 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1892 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1893 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1894 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 1895 ||∇f(.)|| = 0.0015 f(.) = 0.000022 \n",
      "iter = 1896 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1897 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1898 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1899 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1900 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1901 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1902 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1903 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1904 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1905 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1906 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1907 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1908 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1909 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1910 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1911 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1912 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1913 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1914 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1915 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1916 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1917 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1918 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1919 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1920 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1921 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1922 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1923 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1924 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1925 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1926 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1927 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1928 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1929 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1930 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1931 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1932 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1933 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1934 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1935 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1936 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1937 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1938 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1939 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1940 ||∇f(.)|| = 0.0015 f(.) = 0.000021 \n",
      "iter = 1941 ||∇f(.)|| = 0.0014 f(.) = 0.000021 \n",
      "iter = 1942 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1943 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1944 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1945 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1946 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1947 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1948 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1949 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1950 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1951 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1952 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1953 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1954 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1955 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1956 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1957 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1958 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1959 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1960 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1961 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1962 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1963 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1964 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1965 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1966 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1967 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1968 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1969 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1970 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1971 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1972 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1973 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1974 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1975 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1976 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1977 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1978 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1979 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1980 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1981 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1982 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1983 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1984 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1985 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1986 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1987 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1988 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1989 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1990 ||∇f(.)|| = 0.0014 f(.) = 0.000020 \n",
      "iter = 1991 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1992 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1993 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1994 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1995 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1996 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1997 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1998 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 1999 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n",
      "iter = 2000 ||∇f(.)|| = 0.0014 f(.) = 0.000019 \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1.93251817010263e-5, [5.664758250908916e-18, 0.055753661959421476])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_opt,x_opt = gradient_method_constant(f,g,x0,α,ϵ,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient method with a constant step length for a quadratic function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider the following cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(\\mathbf x) = \\frac{1}{2}\\mathbf x^T \\mathbf Q \\mathbf x + \\mathbf c^T \\mathbf x.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is quite nice about quadratic cost function is that the Lipschitz constant for their gradient is easy to determine –⁠ it is just the lowest upper bound on the curvature, that is, the largest eigenvalue of $\\mathbf Q$. Most often than not the $\\mathbf Q$ matrix is chosen as diagonal, in which case determination of the $L$ constant is super easy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gradient_descent_quadratic_constant (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gradient_descent_quadratic_constant(Q,c,x0,ϵ,N)\n",
    "    x = x0                         # initialization of x\n",
    "    f(x) = 1/2*dot(x,Q*x)+dot(x,c)\n",
    "    fx = f(x)\n",
    "    g(x) = Q*x+c                   # gradient of f() \n",
    "    gx = g(x)\n",
    "    L = maximum(diag(Q))           # maximum curvature (here I assume just diagonal Q, otherwise max(eigvals))\n",
    "    α = 1/L                        # step length\n",
    "    iter = 0\n",
    "    while (norm(gx) > ϵ) && iter <= (N-1)\n",
    "        iter = iter+1\n",
    "        x = x - α*gx\n",
    "        gx = g(x)\n",
    "        fx = f(x)\n",
    "        @printf(\"iter = %3d   ||∇f(x)|| = %6.4e   f(x) = %6.4e\\n\",iter,norm(gx),fx)\n",
    "    end\n",
    "    return fx,x\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here come the data for the particular instance of the problem and some parameters of the solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " -1.0\n",
       " -0.6666666666666666"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = [2, 3]         # the initial vector\n",
    "Q = [1 0; 0 3]      # the positive definite matrix defining the quadratic form\n",
    "c = [1;2]           # the vector defining the linear part\n",
    "\n",
    "ϵ  = 1e-5           # the tolerance\n",
    "N  = 100;           # the maximum number of steps \n",
    "\n",
    "xs = -Q\\c           # the stationary point, automatically the minimizer for posdef Q "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter =   1   ||∇f(x)|| = 2.0000e+00   f(x) = 8.3333e-01\n",
      "iter =   2   ||∇f(x)|| = 1.3333e+00   f(x) = -2.7778e-01\n",
      "iter =   3   ||∇f(x)|| = 8.8889e-01   f(x) = -7.7160e-01\n",
      "iter =   4   ||∇f(x)|| = 5.9259e-01   f(x) = -9.9108e-01\n",
      "iter =   5   ||∇f(x)|| = 3.9506e-01   f(x) = -1.0886e+00\n",
      "iter =   6   ||∇f(x)|| = 2.6337e-01   f(x) = -1.1320e+00\n",
      "iter =   7   ||∇f(x)|| = 1.7558e-01   f(x) = -1.1513e+00\n",
      "iter =   8   ||∇f(x)|| = 1.1706e-01   f(x) = -1.1598e+00\n",
      "iter =   9   ||∇f(x)|| = 7.8037e-02   f(x) = -1.1636e+00\n",
      "iter =  10   ||∇f(x)|| = 5.2025e-02   f(x) = -1.1653e+00\n",
      "iter =  11   ||∇f(x)|| = 3.4683e-02   f(x) = -1.1661e+00\n",
      "iter =  12   ||∇f(x)|| = 2.3122e-02   f(x) = -1.1664e+00\n",
      "iter =  13   ||∇f(x)|| = 1.5415e-02   f(x) = -1.1665e+00\n",
      "iter =  14   ||∇f(x)|| = 1.0276e-02   f(x) = -1.1666e+00\n",
      "iter =  15   ||∇f(x)|| = 6.8510e-03   f(x) = -1.1666e+00\n",
      "iter =  16   ||∇f(x)|| = 4.5673e-03   f(x) = -1.1667e+00\n",
      "iter =  17   ||∇f(x)|| = 3.0449e-03   f(x) = -1.1667e+00\n",
      "iter =  18   ||∇f(x)|| = 2.0299e-03   f(x) = -1.1667e+00\n",
      "iter =  19   ||∇f(x)|| = 1.3533e-03   f(x) = -1.1667e+00\n",
      "iter =  20   ||∇f(x)|| = 9.0219e-04   f(x) = -1.1667e+00\n",
      "iter =  21   ||∇f(x)|| = 6.0146e-04   f(x) = -1.1667e+00\n",
      "iter =  22   ||∇f(x)|| = 4.0097e-04   f(x) = -1.1667e+00\n",
      "iter =  23   ||∇f(x)|| = 2.6731e-04   f(x) = -1.1667e+00\n",
      "iter =  24   ||∇f(x)|| = 1.7821e-04   f(x) = -1.1667e+00\n",
      "iter =  25   ||∇f(x)|| = 1.1881e-04   f(x) = -1.1667e+00\n",
      "iter =  26   ||∇f(x)|| = 7.9204e-05   f(x) = -1.1667e+00\n",
      "iter =  27   ||∇f(x)|| = 5.2803e-05   f(x) = -1.1667e+00\n",
      "iter =  28   ||∇f(x)|| = 3.5202e-05   f(x) = -1.1667e+00\n",
      "iter =  29   ||∇f(x)|| = 2.3468e-05   f(x) = -1.1667e+00\n",
      "iter =  30   ||∇f(x)|| = 1.5645e-05   f(x) = -1.1667e+00\n",
      "iter =  31   ||∇f(x)|| = 1.0430e-05   f(x) = -1.1667e+00\n",
      "iter =  32   ||∇f(x)|| = 6.9535e-06   f(x) = -1.1667e+00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.1666666666424912, [-0.9999930465399322, -0.6666666666666666])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fopt,xopt = gradient_descent_quadratic_constant(Q,c,x0,ϵ,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient method with an exact search for a quadratic function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we want to implement and analyze behavior of the gradient method when an true minimum is search for along the descent direction. We again restrict ourselves to quadratic functions. Our motivation for this restriction was that the minimizer along a fixed direction can be found using a formula in a single step, \n",
    "and the overall minimizer can be found by solving a linear system, hence we can easily compare the outcomes of the iterative algorithm to the \"true\" solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An implementation of the algorithm is below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gradient_descent_quadratic_exact (generic function with 1 method)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gradient_descent_quadratic_exact(Q,c,x0,ϵ,N)\n",
    "    x = x0\n",
    "    f(x) = 1/2*dot(x,Q*x)+dot(x,c)\n",
    "    fx = f(x)\n",
    "    g(x) = Q*x+c\n",
    "    gx = g(x)\n",
    "    iter = 0\n",
    "    while (norm(gx) > ϵ) && iter <= (N-1)\n",
    "        iter = iter+1\n",
    "        α = dot(gx,gx)/dot(gx,Q*gx)\n",
    "        x = x - α*gx\n",
    "        gx = g(x)\n",
    "        fx = f(x)\n",
    "        @printf(\"iter = %3d   ||∇f(x)|| = %6.4e   f(x) = %6.4e\\n\",iter,norm(gx),fx)\n",
    "    end\n",
    "    return fx,x\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can call the solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter =   1   ||∇f(x)|| = 2.0229e+00   f(x) = 7.8495e-01\n",
      "iter =   2   ||∇f(x)|| = 9.0210e-01   f(x) = -1.0123e+00\n",
      "iter =   3   ||∇f(x)|| = 1.6005e-01   f(x) = -1.1544e+00\n",
      "iter =   4   ||∇f(x)|| = 7.1374e-02   f(x) = -1.1657e+00\n",
      "iter =   5   ||∇f(x)|| = 1.2663e-02   f(x) = -1.1666e+00\n",
      "iter =   6   ||∇f(x)|| = 5.6470e-03   f(x) = -1.1667e+00\n",
      "iter =   7   ||∇f(x)|| = 1.0019e-03   f(x) = -1.1667e+00\n",
      "iter =   8   ||∇f(x)|| = 4.4679e-04   f(x) = -1.1667e+00\n",
      "iter =   9   ||∇f(x)|| = 7.9269e-05   f(x) = -1.1667e+00\n",
      "iter =  10   ||∇f(x)|| = 3.5350e-05   f(x) = -1.1667e+00\n",
      "iter =  11   ||∇f(x)|| = 6.2718e-06   f(x) = -1.1667e+00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.1666666666479069, [-0.9999939492423319, -0.6666672167355456])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fopt,xopt = gradient_descent_quadratic_exact(Q,c,x0,ϵ,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now decorate the solver a bit so that it records the solution history for later plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gradient_method_quadratic_exact (generic function with 1 method)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gradient_method_quadratic_exact(Q,r,x0,ϵ,N)\n",
    "    x = x0\n",
    "    X = x\n",
    "    f(x) = 1/2*dot(x,Q*x)+dot(x,r)\n",
    "    fx = f(x)\n",
    "    F = [fx,]\n",
    "    g(x) = Q*x+r\n",
    "    gx = g(x)\n",
    "    iter = 0\n",
    "    while (norm(gx) > ϵ) && iter <= (N-1)\n",
    "        iter = iter+1\n",
    "        α = dot(gx,gx)/dot(gx,Q*gx)\n",
    "        x = x - α*gx\n",
    "        fx = f(x)\n",
    "        gx = g(x)\n",
    "        @printf(\"iter = %3d   ||∇f(x)|| = %4.2e   f(x) = %4.2e   α = %4.2e\\n\",iter,norm(gx),fx,α)\n",
    "        X = hcat(X,x)\n",
    "        push!(F,fx)\n",
    "    end\n",
    "    return F,X\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter =   1   ||∇f(x)|| = 2.02e+00   f(x) = 7.85e-01   α = 3.49e-01\n",
      "iter =   2   ||∇f(x)|| = 9.02e-01   f(x) = -1.01e+00   α = 8.78e-01\n",
      "iter =   3   ||∇f(x)|| = 1.60e-01   f(x) = -1.15e+00   α = 3.49e-01\n",
      "iter =   4   ||∇f(x)|| = 7.14e-02   f(x) = -1.17e+00   α = 8.78e-01\n",
      "iter =   5   ||∇f(x)|| = 1.27e-02   f(x) = -1.17e+00   α = 3.49e-01\n",
      "iter =   6   ||∇f(x)|| = 5.65e-03   f(x) = -1.17e+00   α = 8.78e-01\n",
      "iter =   7   ||∇f(x)|| = 1.00e-03   f(x) = -1.17e+00   α = 3.49e-01\n",
      "iter =   8   ||∇f(x)|| = 4.47e-04   f(x) = -1.17e+00   α = 8.78e-01\n",
      "iter =   9   ||∇f(x)|| = 7.93e-05   f(x) = -1.17e+00   α = 3.49e-01\n",
      "iter =  10   ||∇f(x)|| = 3.53e-05   f(x) = -1.17e+00   α = 8.78e-01\n",
      "iter =  11   ||∇f(x)|| = 6.27e-06   f(x) = -1.17e+00   α = 3.49e-01\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([23.5, 0.78494623655914, -1.0122561427192018, -1.1544497921695156, -1.1657000743731913, -1.1665901904237432, -1.1666606159089987, -1.166666187934096, -1.1666666287896128, -1.1666666636698553, -1.1666666664295606, -1.1666666666479069], [2.0 0.9516129032258065 … -0.9999906988353201 -0.9999939492423319; 3.0 -0.8440860215053765 … -0.6666552985765024 -0.6666672167355456])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F,X = gradient_method_quadratic_exact(Q,c,x0,ϵ,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now visualize the function and plot the minimizer computed as the stationary point of the quadratic function. On top of this we plot the individual steps of the gradient algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1_data = x2_data = -4:0.01:4;\n",
    "f(x) = 1/2*dot(x,Q*x)+dot(x,c)\n",
    "z_data = [f([x1,x2]) for x2=x2_data, x1=x1_data];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "contour(x1_data,x2_data,z_data)\n",
    "plot!(X[1,:],X[2,:],label=L\"$\\mathrm{x}_k$\",marker=:diamond,aspect_ratio=1)\n",
    "scatter!([x0[1],],[x0[2],],label=L\"$\\mathrm{x}_0$\")\n",
    "scatter!([xs[1],],[xs[2],],label=L\"$\\mathrm{x}_\\mathrm{opt}$\")\n",
    "xlabel!(L\"$x_1$\");ylabel!(L\"$x_2$\");\n",
    "xlims!(-4,4); ylims!(-4,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also plot the cost function values separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(F[:],label=L\"$f(\\mathrm{x}_k)$\")\n",
    "xlabel!(\"k\")\n",
    "ylabel!(L\"$f(\\mathrm{x}_k)$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient method with backtracking for a quadratic function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gradient_descent_quadratic_backtracking (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gradient_descent_quadratic_backtracking(Q,c,x0,s,γ,β,ϵ,N)\n",
    "    x = x0\n",
    "    f(x) = 1/2*dot(x,Q*x)+dot(x,c)\n",
    "    fx = f(x)\n",
    "    g(x) = Q*x+c\n",
    "    gx = g(x)\n",
    "    iter = 0\n",
    "    while (norm(gx) > ϵ) && iter <= (N-1)\n",
    "        iter = iter+1\n",
    "        α = s\n",
    "        while (fx-f(x - α*gx)) < γ*α*dot(gx,gx)\n",
    "            α = β*α\n",
    "        end\n",
    "        x = x - α*gx\n",
    "        gx = g(x)\n",
    "        fx = f(x)\n",
    "        @printf(\"iter = %3d   ||∇f(x)|| = %6.4e   f(x) = %6.4e\\n\",iter,norm(gx),fx)\n",
    "    end\n",
    "    return fx,x\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = 1.0; γ = 0.2; β = 0.5;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter =   1   ||∇f(x)|| = 5.7009e+00   f(x) = 5.0000e+00\n",
      "iter =   2   ||∇f(x)|| = 2.8504e+00   f(x) = 3.7500e-01\n",
      "iter =   3   ||∇f(x)|| = 1.4252e+00   f(x) = -7.8125e-01\n",
      "iter =   4   ||∇f(x)|| = 7.1261e-01   f(x) = -1.0703e+00\n",
      "iter =   5   ||∇f(x)|| = 3.5630e-01   f(x) = -1.1426e+00\n",
      "iter =   6   ||∇f(x)|| = 1.7815e-01   f(x) = -1.1606e+00\n",
      "iter =   7   ||∇f(x)|| = 8.9076e-02   f(x) = -1.1652e+00\n",
      "iter =   8   ||∇f(x)|| = 4.4538e-02   f(x) = -1.1663e+00\n",
      "iter =   9   ||∇f(x)|| = 2.2269e-02   f(x) = -1.1666e+00\n",
      "iter =  10   ||∇f(x)|| = 1.1135e-02   f(x) = -1.1666e+00\n",
      "iter =  11   ||∇f(x)|| = 5.5673e-03   f(x) = -1.1667e+00\n",
      "iter =  12   ||∇f(x)|| = 2.7836e-03   f(x) = -1.1667e+00\n",
      "iter =  13   ||∇f(x)|| = 1.3918e-03   f(x) = -1.1667e+00\n",
      "iter =  14   ||∇f(x)|| = 6.9591e-04   f(x) = -1.1667e+00\n",
      "iter =  15   ||∇f(x)|| = 3.4795e-04   f(x) = -1.1667e+00\n",
      "iter =  16   ||∇f(x)|| = 1.7398e-04   f(x) = -1.1667e+00\n",
      "iter =  17   ||∇f(x)|| = 8.6988e-05   f(x) = -1.1667e+00\n",
      "iter =  18   ||∇f(x)|| = 4.3494e-05   f(x) = -1.1667e+00\n",
      "iter =  19   ||∇f(x)|| = 2.1747e-05   f(x) = -1.1667e+00\n",
      "iter =  20   ||∇f(x)|| = 1.0874e-05   f(x) = -1.1667e+00\n",
      "iter =  21   ||∇f(x)|| = 5.4368e-06   f(x) = -1.1667e+00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.1666666666610581, [-0.9999985694885254, -0.6666684150695801])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fopt,xopt = gradient_descent_quadratic_backtracking(Q,c,x0,s,γ,β,ϵ,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A decorated version of the algorithm follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gradient_method_quadratic_backtracking (generic function with 1 method)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gradient_method_quadratic_backtracking(Q,c,x0,s,γ,β,ϵ,N)\n",
    "    x = x0\n",
    "    X = x\n",
    "    f(x) = 1/2*dot(x,Q*x)+dot(x,c)\n",
    "    fx = f(x)\n",
    "    F = [f(x),]\n",
    "    g(x) = Q*x+c\n",
    "    gx = g(x)\n",
    "    iter = 0\n",
    "    while (norm(g(x)) > ϵ)\n",
    "        iter = iter+1\n",
    "        α = s\n",
    "        while (fx-f(x - α*gx)) < γ*α*norm(gx)^2\n",
    "            α = β*α\n",
    "        end\n",
    "        x = x - α*gx\n",
    "        fx = f(x)\n",
    "        gx = g(x)\n",
    "        @printf(\"iter = %3d   ||∇f(x)|| = %4.2e   f(x) = %4.2e   t = %4.2e\\n\",iter,norm(gx),fx,α)\n",
    "        X = hcat(X,x)\n",
    "        push!(F,fx)\n",
    "        if iter >= N\n",
    "         return F,X\n",
    "        end\n",
    "    end\n",
    "    return F,X\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter =   1   ||∇f(x)|| = 5.70e+00   f(x) = 5.00e+00   t = 5.00e-01\n",
      "iter =   2   ||∇f(x)|| = 2.85e+00   f(x) = 3.75e-01   t = 5.00e-01\n",
      "iter =   3   ||∇f(x)|| = 1.43e+00   f(x) = -7.81e-01   t = 5.00e-01\n",
      "iter =   4   ||∇f(x)|| = 7.13e-01   f(x) = -1.07e+00   t = 5.00e-01\n",
      "iter =   5   ||∇f(x)|| = 3.56e-01   f(x) = -1.14e+00   t = 5.00e-01\n",
      "iter =   6   ||∇f(x)|| = 1.78e-01   f(x) = -1.16e+00   t = 5.00e-01\n",
      "iter =   7   ||∇f(x)|| = 8.91e-02   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =   8   ||∇f(x)|| = 4.45e-02   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =   9   ||∇f(x)|| = 2.23e-02   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  10   ||∇f(x)|| = 1.11e-02   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  11   ||∇f(x)|| = 5.57e-03   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  12   ||∇f(x)|| = 2.78e-03   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  13   ||∇f(x)|| = 1.39e-03   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  14   ||∇f(x)|| = 6.96e-04   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  15   ||∇f(x)|| = 3.48e-04   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  16   ||∇f(x)|| = 1.74e-04   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  17   ||∇f(x)|| = 8.70e-05   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  18   ||∇f(x)|| = 4.35e-05   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  19   ||∇f(x)|| = 2.17e-05   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  20   ||∇f(x)|| = 1.09e-05   f(x) = -1.17e+00   t = 5.00e-01\n",
      "iter =  21   ||∇f(x)|| = 5.44e-06   f(x) = -1.17e+00   t = 5.00e-01\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([23.5, 5.0, 0.375, -0.78125, -1.0703125, -1.142578125, -1.16064453125, -1.1651611328125, -1.166290283203125, -1.1665725708007812  …  -1.1666651964187622, -1.1666662991046906, -1.1666665747761726, -1.1666666436940432, -1.1666666609235108, -1.1666666652308777, -1.1666666663077194, -1.1666666665769299, -1.1666666666442325, -1.1666666666610581], [2.0 0.5 … -0.9999971389770508 -0.9999985694885254; 3.0 -2.5 … -0.6666631698608398 -0.6666684150695801])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F,X = gradient_method_quadratic_backtracking(Q,c,x0,s,γ,β,ϵ,N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "contour(x1_data,x2_data,z_data)\n",
    "plot!(X[1,:],X[2,:],label=L\"$\\mathrm{x}_k$\",marker=:diamond)\n",
    "scatter!([x0[1],],[x0[2],],label=L\"$\\mathrm{x}_0$\")\n",
    "scatter!([xs[1],],[xs[2],],label=L\"$\\mathrm{x}_\\mathrm{opt}$\")\n",
    "xlabel!(L\"$x_1$\");ylabel!(L\"$x_2$\");\n",
    "xlims!(-4,4); ylims!(-4,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(F[:],label=L\"$f(\\mathrm{x}_k)$\")\n",
    "xlabel!(\"k\")\n",
    "ylabel!(L\"$f(\\mathrm{x}_k)$\")"
   ]
  }
 ],
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   "lastKernelId": null
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   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
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   "labels_anchors": false,
   "latex_user_defs": false,
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  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
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   "toc_position": {
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    "left": "10px",
    "top": "150px",
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   "toc_section_display": true,
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  "varInspector": {
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   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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