k = 0
tinit = 1.0
y = 1.5
e = 0.1

A = [0.4873 -0.8732;
    0.6072 0.7946;
    0.9880 -0.1546;
    -0.2142 -0.9768;
    -0.9871 -0.1601;
    0.9124 0.4093]

b = [1;
    1;
    1;
    1;
    1;
    1]

c = [1;
    -1]

x0 = [0, 0]

V = [0.1562 0.9127 1.0338 0.8086 -1.3895 -0.8782;
    -1.0580 -0.6358 0.1386 0.6406 2.3203 -0.8311]

[m, n] = size(A)

t = tinit

%t*c'*x - sum(log(b-A*x))
%t*c + (A')*(1./(b-A*x))
%((diag(1./(b-A*x))*A)')*(diag(1./(b-A*x))*A)


%cvx_begin

%cT = c'

%variable x(n)
%minimize cT*x
%subject to
%    A*x <= b

%cvx_end

xk = x0
%temp = xk
cT = c'

while m/t >= e
    k
    cvx_begin

    variable x(n)
    minimize t*cT*x - sum(log(b-A*x))

    cvx_end

    %temp = xk
    xk = [xk;x']
    %xk = temp

    k = k + 1
    t = y*t
end

m/t
xk

t*cT*xk(2) - sum(log(b-A*xk(2)))

%function [f,g,H] = objective_barrier(t,x,A,b,c);
%[m,n] = size(A);
%d = A*x - b; D = diag(1./d);
%f = t*c’*x - log(-d’)*ones(m,1);
%g = t*c - A’*D*ones(m,1);
%H = A’*D^2*A;



figure(1)
%set(gcf,'position',[10,10,560,540])
%fill(V(1,:), V(2,:), 'r')

%grid on
%axis([-2.5 2 -1.5 3])
%xticks(-2.5:0.5:2)
%yticks(-1.5:0.5:3)
%axis equal

x1 = -2.5:0.01:2.0
x2 = -1.5:0.01:3.0
[X1,X2] = meshgrid(x1,x2);
Z = arrayfun(@fbar,X1,X2)
v = [-0.6,0.12,0.24]
contour(X1,X2,Z,v)

function y = fbar(x1,x2)
    A = [0.4873 -0.8732;
    0.6072 0.7946;
    0.9880 -0.1546;
    -0.2142 -0.9768;
    -0.9871 -0.1601;
    0.9124 0.4093];

    b = [1;
    1;
    1;
    1;
    1;
    1];
    if sum(b-A*[x1;x2]<0) == 0
        y = -sum(log(b-A*[x1;x2]));
    else
        y = NaN;
    end
end