lagrange multipiers in matlab

To use Lagrange multipliers in MATLAB, you need to define your objective function and your constraints.

Let's say you have an objective function f(x,y) and a constraint g(x,y) = 0. You can use Lagrange multiplier lambda to solve this constrained optimization problem.

Here's an example code to solve this problem using the fmincon function in MATLAB:

main.m
% Define the objective function and constraint
f = @(x,y) x^2 + y^2;
g = @(x,y) x + y - 1;

% Define the Lagrangian function
L = @(x,y,lambda) f(x,y) - lambda*g(x,y);

% Use fmincon to solve the problem
[x,fval] = fmincon(@(x,y) L(x,y,lambda), [0,0], [], [], [], [], [], [], @(x) mycon(x));

% Define the constraint function
function [c,ceq] = mycon(x)
    % inequality constraint, set to empty
    c = [];
    % equality constraint
    ceq = x(1) + x(2) - 1; 
end
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In this code, fmincon is used to minimize the Lagrangian function using a constrained optimization routine. The mycon function is defined to include the constraint g(x,y) = 0.

The output x corresponds to the values of x and y that minimize the objective function subject to the given constraint. The output fval corresponds to the value of the objective function at the minimum.