how to minimize a function with bounds in matlab

To minimize a function with bounds in Matlab, you can use the fmincon function. This function minimizes a constrained nonlinear multivariable function, subject to optional linear constraints and variable bounds.

Here's an example code:

main.m
% Define the function to minimize
fun = @(x) x(1)^2 + x(2)^2;

% Set the lower and upper bounds for the variables
lb = [-1, -1];
ub = [1, 1];

% Call the fmincon function to minimize the function
x0 = [1, 1]; % initial guess
x = fmincon(fun, x0, [], [], [], [], lb, ub);

% Display the results
fprintf('Minimum found at (%f, %f)\n', x(1), x(2));
fprintf('Objective function value: %f\n', fun(x));
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In this example, we define the function to minimize (fun = @(x) x(1)^2 + x(2)^2), set the lower and upper bounds for the variables (lb = [-1, -1]; ub = [1, 1]), and call the fmincon function to minimize the function given the bounds. The [] inputs specify that we do not have any linear constraints to include.

Finally, we display the results of the optimization.