find the local extrema of multivariable function in matlab

In Matlab, you can use the fminsearch or fminunc functions to find local extrema of a multivariable function. Here's an example:

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

% Initial guess
x0 = [1 1];

% Find local minimum
[x, fval] = fminsearch(f, x0)

% Find local minimum using fminunc
options = optimoptions(@fminunc,'Algorithm','quasi-newton');
x = fminunc(f, x0, options)
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In this example, we define a function f that takes a 2-element vector as input and returns a scalar value. We then use fminsearch to find the input that minimizes f. The function fminunc works similarly, but can handle more complex functions and allows for more options to be specified.

Note that these functions only find local extrema, and may not find the global minimum. To improve the chances of finding the global minimum, you can try running these functions with multiple initial guesses.