write a script to study the unconstrained minimum of function f(x; y) = ¡e x¡y (x 2 ¡ 2y 2 ) in matlab

To write a script to study the unconstrained minimum of the function f(x; y) = ¡exp(x-y) * (x^2 - 2y^2) in MATLAB, you can use the optimization toolbox functions provided by MATLAB. Specifically, the fminunc function can be used to find the unconstrained minimum.

Here is an example script that demonstrates how to use fminunc to minimize the given function:

main.m
% Define the objective function
f = @(x) -exp(x(1)-x(2)) * (x(1)^2 - 2*x(2)^2);

% Initial guess for the minimum
x0 = [0; 0];

% Set the options for fminunc
options = optimoptions('fminunc', 'Display', 'iter');

% Call fminunc to find the minimum
[x, fval] = fminunc(f, x0, options);

% Display the results
disp('Minimum point:');
disp(x);
disp('Minimum value:');
disp(fval);
376 chars
18 lines

In this script, the objective function f is defined using an anonymous function. The initial guess for the minimum is set as x0. The optimoptions function is used to set the display option for fminunc. Finally, fminunc is called with the objective function f, initial guess x0, and options to find the minimum point x and its corresponding value fval. The results are then displayed.

Make sure you have the optimization toolbox installed in MATLAB to use the fminunc function.