simp_op.matlab

clear all;
clc;
%% Parameters
cvx_expert true;
a = 3;
J = 5;
c1 = 1;
c2 = 2;
y = 2;



%% Original CVX Problem


cvx_begin quiet
    variable f
    variable Z
    minimize(c1*(y-f*a)^2 + c2*(f*a)^2 - log(Z))
    subject to
        Z >= 0;
        f*J == Z
cvx_end
f
Z


%% New CVX Problem

lambda = 10;
lim = 50;

% q(lambda)
for i = 1:lim
    % solve J1
    cvx_begin quiet
        variable f_new
        minimize(c1*(y-f_new*a)^2 + c2*(f_new*a)^2 + lambda*(f_new*J))
    cvx_end
    fnew(i) = f_new;
    fopt(i) = c1*(y-f_new*a)^2 + c2*(f_new*a)^2 + lambda*(f_new*J);

    % solve J2
    cvx_begin quiet
        variable Z_new
        minimize(-log(Z_new) - lambda*Z_new)
        subject to
            Z_new >= 0;
    cvx_end
    znew(i) = Z_new;
    zopt(i) = -log(Z_new) - lambda*Z_new;
    
    % update lambda
    cvx_begin quiet
        variable lam
        maximize(c1*(y-f_new*a)^2 + c2*(f_new*a)^2 -log(Z_new) - lam*Z_new + lam*(f_new*J))
    cvx_end
    lamm(i) = lam;
    lopt(i) = c1*(y-f_new*a)^2 + c2*(f_new*a)^2 -log(Z_new) - lam*Z_new + lam*(f_new*J);
    lambda = lam;
end

f_new
Z_new
lambda