clear all; close all; clc;

%% Gradient method for solving a quadratic optimization problem

%% Exercise 4

Q = [6     0    -4     0
     0     6     0    -4
    -4     0     6     0
     0    -4     0     6];

c = [ 1 ; -1 ; 2 ; -3 ] ;

x0 = [ 0 ; 0 ; 0 ; 0 ] ;

tol = 1e-6 ;

%% method

fprintf('Gradient method\n\n');
fprintf('iter \t f(x) \t\t ||grad f(x)||\n\n');

iter = 0 ;

% starting point
x = x0;

while true
    v = 0.5*x'*Q*x + c'*x;
    g = Q*x + c ;
    fprintf('%1.0f \t %1.6f \t %1.7f\n',iter,v,norm(g));
    
    % stopping criterion
    if norm(g) < tol
        break
    end
    
    %   search direction
    d = -g;
    
    %   step size
    t = norm(g)^2/(g'*Q*g) ;
    
    %   new point
    x = x + t*d ;
    iter = iter + 1 ;
end