how to minimize a function with linear constraints and bounds in matlab

To minimize a function with linear constraints and bounds in MATLAB, we can use the "fmincon" function. This function finds the minimum of a constrained nonlinear multivariable function.

Here is an example code:

main.m
% define objective function
fun = @(x) x(1)^2 + x(2)^2;

% set initial guess
x0 = [1, 2];

% set linear constraints
A = [1, 2];
b = 5;

% set bounds
lb = [-10, -10];
ub = [10, 10];

% call fmincon function
x = fmincon(fun,x0,A,b,[],[],lb,ub);

% print the result
disp(x);
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In this example, we define a two-variable objective function "fun", and set the initial guess "x0". We also set the linear constraint "A*x <= b", where A is a 1x2 matrix and b is a scalar. We also set the lower and upper bounds of the variables "x" using "lb" and "ub".

Then, we use the "fmincon" function to find the minimum of the "fun" function subject to the given constraints and bounds. The output "x" contains the values of the variables that minimize the function.

Note that "fmincon" requires the optimization toolbox.