clear
clc
%ANALITYCZNIE
f = @(x) (x(1)+10*x(2))^2 + 5*(x(3)-x(4))^2 + (x(2)-2*x(3))^4 + 10*(x(1)-x(4))^4;
x0 = [3 -1 0 1]';
eps = 0.0001;

g = @(x) [2*x(1)+20*x(2)+40*(x(1)-x(4))^3;
          20*x(1)+200*x(2)+4*(x(2)-2*x(3))^3;
          10*x(3)-10*x(4)-8*(x(2)-2*x(3))^3;
          10*x(4)-10*x(3)-40*(x(1)-x(4))^3];

h = @(x) [120*(x(1)-x(4))^2+2 20 0 -120*(x(1)-x(4))^2;
            20 12*(x(2)-2*x(3))^2+200 -24*(x(2)-2*x(3))^2 0;
            0 -24*(x(2)-2*x(3))^2 48*(x(2)-2*x(3))^2+10 -10;
            -120*(x(1)-x(4))^2 0 -10 120*(x(1)-x(4))^2+10];


for i = 1:100
    x = x0 - (h(x0)^-1)*g(x0);
    if(norm(g(x))<=eps)
        break
    end
    x0 = x;
end
x_ana(1,:) = x;

%CVX
cvx_begin
variable x(4)
minimize ((x(1)+10*x(2))^2 + 5*(x(3)-x(4))^2 + (x(2)-2*x(3))^4 + 10*(x(1)-x(4))^4)
cvx_end
x_cvx = x;

%fminsearch
x0 = [3 -1 0 1]';
x_fmin = fminsearch(f,x0);