Question

1. The function f(z, y) (a-x)2 + b(y-12)2 is called Rosenbrock's banana function. It is often used as a benchmarking test for optimization algorithms becatse it is easy to find the minimum by hand but often very difficult to find numerically. Throughout the problem, we will use the values a = 2 and b 10. You can plot this function using the following code: x3:0.1:3; y = -10:0.2:10; Cx,Ymeshgrid(x,y); Z(2-X).2 10* (Y-X. 2). 2; surf (X, Y,z) (a) Write a Matlab function that computes f using only one input (i.e. one vari- able). Your input wil need to be a vector of length 2. Use this function to calculate f (1, 10) and save the result in A1.dat. (b) Use fminsearch to find the minimum of f and save it as a 2x 1 column vector [x; yl in the file A2.dat. Use an initial guess of [1; 10]

please solve then upload matlab code

Thanks

Answer 1

Q1.

HOME PLOTS APPS EDITOR PUBLISHH MEW Search Documentation Log In Find Files Compare Print Insert Run Section Go To▼ Comment 96 New Open Save Breakpoints Run Run andAdvance Run and Find NAMGA Indent Advance Time FILE BREAKPOINT RUN ÷ H Current Folder /> Users+ debangshasarkar Desktop coursera Deba MATLAB Editor-/Users/debangshasarkar/Desktop/coursera/Deba MATLAB/code2.m Workspace Name ▲ Name ▲ codel.m code2.m matlab.mt 3fx) sample2.csv 1- 2- f= x= @(x) (2-x(1))"2 +10* { x( 2)-x(1)^2)^2 ; [1:101; ans Command Window > code2 ans = 811

Q2.

Here the fminsearch function is used and the minimum values are stored in the column vector z.

HOME PLOTS APPS EDITOR PUBLISHH MEW ( Search Documentation Log In Find Files Insert Run Section E, compare dGoTo. Comment & As -Find New Open Save Breakpoints Run Run andAdvance Run and Print Indent Time FILE NAVIC A BREAKPOINT RUN Workspace Name Current Folder Editor-/Users/debangshasarkar/Desktop/course ra/Deba MATLAB/code2.m 1- f=@(x) (2-x(1))"2+10* (x(2)-x(1)^2)^2 ; 3-Zfminseachf,x) Name ▲ codel.m code2.m ans sample2.cSv Command Window 2> code2 2.0000 4.0000 ans = 2.0080 z(2) 4.0000