Simplified Nelder-Mead method

neldermead.m

f = @(x,y) 100*(x.^2-y).^2 + (x-1).^2;   % Rosenbrock's function
x = -2:0.1:2;
y = -2:0.1:2;
[X,Y] = meshgrid(x,y);
contour (x,y, f(X,Y), 30); 
hold on

T = [-2 -1; 2 0; -1 1];
for i = 1:3
    z(i) = f(T(i,1),T(i,2));
end

tol = 1e-6;
n = 0;
while (true)
    h = fill(T(:,1),T(:,2),'k');
    set(h, 'FaceAlpha', 0);
    [z,ix] = sort(z,'descend');
    T =T(ix,:);
    if z(1)-z(3) < tol
        disp(sprintf('Minimum found at (%.3f, %.3f) after %.d steps', T(3,1),T(3,2),n));
        break;
    end
    R = T(2,:)+T(3,:)-T(1,:);
    fR = f(R(1),R(2));
    if fR < z(3)
        E = 1.5*T(3,:)+1.5*T(2,:)-2*T(1,:);
        fE = f(E(1),E(2));
        if fE < fR
            T(1,:) = E;
            z(1) = fE;
        else 
            T(1,:) = R; 
            z(1) = fR;
        end
    else
        for i=1:2
            T(i,:) = (T(i,:)+T(3,:))/2;
            z(i) = f(T(i,1),T(i,2));
        end
    end
    n = n+1;
    if n>= 200
        disp('Failed to converge'); break;
    end
end