An example of fmincon returning Hessian for linear model

fmincon_example

clear g

T = 10;
m_exact = 1;
b_exact = 2;
x_exact = [m_exact; b_exact]

t = [0:T-1]/(T-1);

A = [t' ones(size(t'))];

y_exact = A*x_exact;

figure(1)
plot(t,y_exact,'-o')

G = @(x) (y_exact-A*x)'*(y_exact-A*x);


m = [.5:.01:3];
b = [.5:.01:3];
[mm,bb] = meshgrid(m,b);

mm = mm(:);bb = bb(:);


for i = 1:length(mm)
    g(i) = G([mm(i);bb(i)]);
end

figure(2)
g = reshape(g,length(m), length(b));
imagesc(m,b,g)
xlabel('m')
ylabel('b')

x0 = [4.5;2.2];
[x_est,fval,flag,output,grad,hessian] = fminunc(G,x0);

theoretical_hessian = 2*A'*A;

disp(x_exact)
disp(x_est)

disp(theoretical_hessian)
disp(hessian)