fmincon example

gistfile1.matlab

function [c, ceq] = h(x)
    ceq = [];
    c = (x(1) - 1)^2 + (x(2) + 1)^2 - 1;
end

function [xp, yp] = circle(x,y,r)
    ang=0:0.01:2*pi; 
    xp= x + r * cos(ang);
    yp= y + r * sin(ang);
end

function zad4()
    fun = @(x) x(1)^3 + x(1)^2 + x(1)*x(2) + x(2)^2;
    
    x0 = [0, 0];
    
    [xopt, min] = fmincon(fun, x0, [], [], [], [], [], [], @h);
    xopt
    min   
    
    N = 75;
    elems = 100;
    
    [x1, x2] = meshgrid(linspace(-0.7, 0.7, elems), linspace(-0.7, 0.7, elems));
    y = x1.^3 + x1.^2 + x1*x2 + x2.^2;
    
    figure();
    hold on;
    xlabel('x1');
    ylabel('x2');
    title('Wykres poziomnicowy funkcjonału jakości.');
    grid on;
    contour(x1, x2, y, N);
    plot(xopt(1), xopt(2), '*');
    [cx, cy] = circle(1, -1, 1);
    plot(cx, cy, '--k', 'LineWidth', 2);
    hold off; 
end