clc;
clear;


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Example of optimization subject to inequality constraints
%
% PROBLEM:
% Max_{C,L,N} log(C) + aL
% s.t.:
% C <= w*N
% L + N <= 1
% {C,L,N} >= 0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% parameters:
a = 0.3; % marginal utility of leisure
w = 2; % wage

params = [a;w];

% X = [C;L;N]
% Initial guess for the solution
X0 = 0.5*ones(3,1);

% time constraint (linear) A*X <= b
A = [0 1 1];
b = 1;

% non-negativity constraint:
lb = zeros(3,1); 

[X1,fval,exitflag,output,lambda,grad,hessian] = fmincon(@(X)objective(X,params),X0,A,b,[],[],lb,[],@(X)nonlcon(X,params))