clear all
close all
clc
x=-5:0.1:5;
y=-5:0.1:5;
f=@(x,y)2*x.^2+y.^2+x.*y-6*x-5*y+8;
lambda=0.2;
[X,Y]=meshgrid(x);
contour(x,y,f(X,Y),50)
x0=-4;
y0=-4;



while(i~=1)
    y1=f(x0,y0);
    y2=f(x0-lambda,y0);
    y3=f(x0,y0+lambda);
    y4=f(x0+lambda,y0);
    y5=f(x0,y0-lambda);

    [ymin,i]=min([y1;y2;y3;y4;y5]);
    hold on
        if     (i==2)
                line([x0,x0],[y0,y0])
                plot(x0-lambda,y,'')
                x0=x0-lambda;
        elseif (i==3)
                plot(x0,y0+lambda,'bo')
                y0=y0+lambda;
        elseif (i==4)
                plot(x0+lambda,y0,'go')
                x0=x0+lambda;
        elseif (i==5)
                plot(x0,y0-lambda,'yo')
                y0=y0-lambda;

    end
end
hold off
x0
y0