Find min in Gradient Matlab

gaussseidel.m

close all; clear all; clc;

eps = 0.01;
x0 = -4;
y0 = -4;

F = @(x,y)(x.^2).*2 + y.^2 + x.*y - x.*6 - y.*5 + 8;

x = linspace(-5, 5);
y = linspace(-5, 5);

[X, Y] = meshgrid(x, y);
Z = F(X, Y);
contour(X, Y, Z, 50);
hold on;
grid on;

v0 = [x0, y0];
v1 = [x0 - 1, y0 - 1];

counter = 0;

while true
    prevX = v0(1);
    prevY = v0(2);
    
    counter = counter + 1;

    % Y's
    F=@(y)2*v0(1).^2 + y.^2 + v0(1).*y - 6*v0(1) - 5*y + 8;
    
    result = calc(F, -5, 5, v0(2), v1(2));
    v0(2) = result(1);
    v1(2) = result(2);    
    
    plotPoint(v1(1), v1(2));
    plotLine([v0(1),v0(1)],[prevY,v0(2)]);
    
    % X's
    F=@(x)2*x.^2 + v0(2).^2 + x*v0(2) - 6*x - 5*v0(2) + 8;
    
    result = calc(F, -5, 5, v0(1), v1(1));
    v0(1) = result(1);
    v1(1) = result(2);
    
    plotPoint(v0(1), v0(2));
    plotLine([prevX, v0(1)],[v0(2),v0(2)]);
         
    fprintf("Iter: %i \n", counter);
    printPoint(v0(1), v0(2));
    printPoint(v1(1), v1(2));
    fprintf("\n");
    
    if diff(v0, v1) < eps
        % fprintf("break \n");
        break;
    end
end

function printPoint(x, y)
    fprintf("x: %0.2f, y: %0.2f \n", x, y);
end

function plotPoint(x, y)
    plot(x,y,'r.');
end

function plotLine(from, to)
    line(from, to, 'Color','black');
end

function result = calc(F, a, b, n0, n1) 
    eps = 0.01;
    
    a1=(((a+b)/2) + a) / 2;
    a2=(((a+b)/2) + b) / 2;
    
    while b - a > eps 
        if F(a1)<F(a2) 
            b = a2;
        else
            a = a1;
        end
        a1=(((a+b)/2)+a)/2;
        a2=(((a+b)/2)+b)/2;
    end
    
    n1=n0;
    n0=(a1+a2) / 2;
    
    result = [n0, n1];
end

function result = diff(v0, v1)
    result = sqrt((v1(1) - v0(1)).^2 + ((v1(2) - v0(2)).^2));
end

min2d.m

close all; clear all; clc;

% const
alpha = 0.2;
x0 = -4;
y0 = -4;

F = @(x,y) (x.^2).*2 + y.^2 + x.*y - x.*6 - y.*5 + 8;

x = linspace(-5, 5);
y = linspace(-5, 5);

[X, Y] = meshgrid(x, y);
Z = F(X, Y);
contour(X, Y, Z, 50);
hold on;

flag = 1;

while flag == 1
    flag = 0;
   
    vecA = [
        0
        y0 + alpha
        x0 + alpha
        y0 - alpha
        x0 - alpha
    ];

    vecF = [
        F(x0, y0)
        F(x0, vecA(2))
        F(vecA(3), y0)
        F(x0, vecA(4))
        F(vecA(5), y0)
    ];

    [ymin, i] = min(vecF);

    if i > 1
        if i == 2 || i == 4
            y0 = vecA(i);
        end

        if i == 3 || i == 5
            x0 = vecA(i);
        end
        
        flag = 1;
    end

    plot(x0, y0, 'r.');
    
end

fprintf("x: %0.2f, y: %0.2f \n", x0, y0);

simplegrad.m

eps = 0.1;
lambda = 0.1;

F = @(x,y)(x.^2).*2 + y.^2 + x.*y - x.*6 - y.*5 + 8;

x = linspace(-5, 5);
y = linspace(-5, 5);

x0 = 5;
y0 = 5;

[X, Y] = meshgrid(x, y);
Z = F(X, Y);
contour(X, Y, Z, 50);
hold on;
grid on;

vn = [x0, y0];

for n=1:100
    
    grad = GradF(vn(1), vn(2));
    
    gradnorm = norm(grad);
    
    n_grad = grad / gradnorm;
    
    vn1 = vn - n_grad.*lambda;
    
    fprintf("%d: [ %.2f, %.2f ] \n", n, vn1(1), vn1(2));
    
    plotPoint(vn1(1), vn1(2));
    
    % fprintf("diff: %.5f \n", gradnorm - eps)
    
    if gradnorm - eps < 0
       break; 
    end
    
    vn = vn1;
end

function plotPoint(x, y)
    plot(x,y,'r.');
end

function result = GradF(x, y)
    dfx = x.*4 + y - 6;
    dfy = y.*2 + x - 5;  
    
    result = [dfx, dfy];
end