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%%
% Simple test for Frank-Wolfe algorithm
rep = '../results/frank-wolfe/';
[~,~] = mkdir(rep);
test = 2;
% square
K = [-1-1i; -1+1i; 1+1i; 1-1i];
% polygon
m = 3;
K = exp( 1i*pi/m + 2i*pi * (0:m-1)'/m );
% function
switch test
case 1
p0 = 1+.3i; % target point
case 2
p0 = 0;
end
f = @(z)1/2*abs(z-p0).^2;
df = @(z)z-p0;
dotp = @(u,v)real(u*conj(v));
% draw
q = 256;
x = linspace(-1.05,1.05,q);
y = linspace(-.9,.9,q);
[Y,X] = meshgrid(y,x);
F = f(X+1i*Y);
niter = 18;
Z = [];
% initialize farthest possible
[~,i] = max(f(K));
z = K(i);
z = K(2);
clf; hold on;
imagesc(x,y,F');
plot(K([1:end 1]), 'k.-', 'MarkerSize', 25, 'LineWidth', 2);
for i=1:niter
Z(i) = z;
d = df(z);
% find extremal point
u = K(1);
for j=1:length(K)
if dotp(d,K(j))<dotp(d,u)
u = K(j);
end
end
% update
gamma = 2/(2+i);
z = z + gamma*(u-z);
% draw
t = (i-1)/(niter-1);
plot([Z(end) z], '.-', 'color', [t 0 1-t], 'LineWidth', 2, 'MarkerSize', 25);
end
clf; hold on;
% background function
r = 20;
imagesc(x,y,F');
contour(x,y,F',r, 'k');
colormap(parula(r+1));
%
plot(K([1:end 1]), 'k.-', 'MarkerSize', 25, 'LineWidth', 2);
plot(real(p0), imag(p0), 'r.', 'MarkerSize', 25);
for i=1:niter-1
t = (i-1)/(niter-2);
plot(Z(i:i+1), '.-', 'color', [t 0 1-t], 'LineWidth', 2, 'MarkerSize', 25);
end
axis off; axis equal
saveas(gcf, [rep 'fw-' num2str(test) '.png']);