find the minimum of f(x,y) in matlab

There are different optimization methods available in Matlab to find the minimum of a function. Here is an example with the fminsearch function:

main.m
% define the function to minimize
f = @(x) (x(1)-2)^2 + (x(2)+3)^2;

% initial guess
x0 = [0,0];

% minimize the function using fminsearch
[xopt, fval] = fminsearch(f, x0);

% display the optimal solution and function value
disp(['optimal solution: x = ', num2str(xopt)])
disp(['minimum value: f(x) = ', num2str(fval)])
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In this example, we define the function f(x,y) as the sum of two squared terms. We then use the fminsearch function to find the minimum of f starting from the initial guess x0. The output of fminsearch contains the optimal solution (xopt) and the minimum value (fval) of the function.