how to maximize a function with bounds in matlab

To maximize a function with bounds in MATLAB, you can use the "fmincon" function which is a built-in optimization function for constrained minimization. However, since we want to maximize the function, we need to convert the maximization problem into a minimization problem by multiplying the function by -1.

Here is an example code for maximizing a function with upper and lower bounds using "fmincon":

main.m
% Define the function to be maximized
fun = @(x) -x(1)^2 - x(2)^2;
% Define the lower bounds
lb = [0,0];
% Define the upper bounds
ub = [10,10];

% Set up the options for the optimization function
options = optimoptions('fmincon','Display','iter');

% Call the optimization function
[xmax,fval,exitflag,output] = fmincon(fun,[2,2],[],[],[],[],lb,ub,[],options);
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In this example, we want to maximize the function "f(x) = -x1^2 - x2^2" subject to the bounds "0 <= x1 <= 10" and "0 <= x2 <= 10".

We define the function "fun" as the negative of the function we want to maximize, and we set the lower and upper bounds using the "lb" and "ub" variables.

We also set the options for the optimization function using "optimoptions". In this case, we set the display option to "iter" to show the iteration information during the optimization process.

Finally, we call the "fmincon" function with the function handle "fun", an initial guess of [2,2], and the constraints and options previously defined. The function returns the maximum value "fval", the location of the maximum "xmax", and additional information about the optimization process.