fmincon constraint in matlab

fmincon is a built-in MATLAB optimization solver that solves nonlinear programming problems with non-linear constraints. Constraints can be defined as linear or non-linear inequality/equality functions. Here's an example code snippet that demonstrates how to use fmincon with constraints:

main.m
% Define objective function and initial guess
fun = @(x) 100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
x0 = [-1,2];

% Define inequality constraints 
A = [1,1];
b = 1;

% Define options for fmincon solver
options = optimoptions('fmincon','Display','iter');

% Solve with fmincon
[x,fval,exitflag,output] = fmincon(fun,x0,A,b,[],[],[],[],[],options);
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In the above code:

• fun is the objective function to be minimized
• x0 is the initial guess for the solver to start the minimization
• A,b define the linear inequality constraint
• options defines the solver options.
• x is the output, the optimized decision variables that minimize the given objective function.
• fval is the optimal objective function value of fun found by fmincon
• exitflag is an output that indicates the exit condition of the solver
• output is a structure containing output about the number of function evaluations, algorithm iterations, etc.

Please refer to MATLAB documentation for more detailed explanation of the fmincon usage and syntax.