Question

(MATLAB): Suppose that you are given a positive definite symmetric matrix A, a vector b, and a real number c. Write MATLAB code which finds the minimum of the function f() r A bc subject to the constraint rT =1 for some vector r and real number . Note: This is a Lagrange Multi pliers problem It turns out that the Lagrange multiplier algebra is simply matrix algebra, which you can easily do in MATLAB. It may be a In particular, consider the function f(r) = x2 + y2 subject to the constraint y = 17. This corresponds to A I, b 0, c= 0, r = [0 1] and n is some umber. This is a problem you can easily do and use to verify your work. I would appreciate it if you would turn in your scratch work for this problem good idea to do a few small cases and see how you can generalize this

Answer 1

MATLAB Script:

close all
clear
clc

A = eye(2); b = 0; c = 0;
r = [0 1]; n = 2;
fmin = findfmin(A,b,c,r,n)

function fmin = findfmin(A,b,c,r,n)
fun = @(x) x'*A*x + b' + c;
x0 = ones(size(A,2), 1); % Initial guess
r = r(:);
Aeq = r'; beq = n; % Equality contraints
[~,fmin] = fmincon(fun, x0, [], [], Aeq, beq); % Contrained minimizer
end

Sample Output:

fmin =
4