create optimization method in matlab

In order to create an optimization method in Matlab, we need to use the built-in function 'fmincon'. This function finds the minimum of a constrained non-linear multivariable function.

Here is a sample code to create an optimization method using 'fmincon':

main.m
% Define the function to optimize
fun = @(x)(x(1)-3)^2 + (x(2)-2)^2;

% Define constraints
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0, 0];
ub = [4, 4];

% Use fmincon
x0 = [0, 0];
options = optimoptions('fmincon','Display','iter');
[x,fval] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,[],options);
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In the above code, we first define the function to optimize, which in this case is (x(1)-3)^2 + (x(2)-2)^2. We then define the constraints using the A, b, Aeq, beq, lb, ub parameters.

Next, we use the 'fmincon' function to find the minimum of the function. We provide the function to optimize, the initial guess x0, and the constraints defined above.

Finally, the function returns the optimized value for x, and the corresponding function value fval.

Keep in mind that fmincon may not always find the global minimum. To ensure that the global minimum is found, multiple runs with different initial guesses should be performed.