Optimal and Robust Control

1. Your own Matlab code for steepest descent and testing with Rosenbrock "banana" function.

Write your own Matlab code implementing a steepest descent search and check its performance using some quadratic functions from previous problems. Finally, check the performance with the Rosenbrock function (also known as banana function), which is given

f(x,y)=(1−x)2+100(y−x2)2

2. Your own Matlab code for Newton method and testing with Rosenbrock "banana" function

Write your own Matlab code implementing a Newton's method and check its performance using some quadratic functions from previous problems. Finally, check the performance with the Rosenbrock function described in the previous examle.

3. Use (and usage) of "fminunc" (Optimization toolbox for Matlab)

Learn how to use the optimization routines contained in Optimization toolbox in Matlab, namely the fminunc function. Unless you are already mastering it, you will have to learn the concept of anonymous functions in Matlab. It is easy. Pay also attention which parameters can be set in order to configure the solver (using the optimset function).