write Projected Gradient project for rosenbrock function ?

[franck olilo]

this my gradient Projection code :

function [x_k,fun_val]= projected_gradient_backtracking(f,g,x0,r,s,alpha,beta,epsilon)

x_k = x0;

grad = g(x_k);

fun_val = f(x_k);

iter = 0;

delta_x = 1;

while (delta_x > epsilon)

iter = iter+1;

t = s;

while f(x_k)-f(proj(x_k-t*grad)) < alpha*t*norm((1/t)*(x_k-proj(x_k-t*grad)))^2 %%% fix

t = beta*t;

end

x_kp1 = proj(x_k-t*grad);

delta_x = norm(x_k - x_kp1);

x_k = x_kp1;

fun_val = f(x_k);

grad = g(x_k);

fprintf('iter_number = %3d norm_grad = %2.6f fun_val = %2.6f \n',iter,delta_x,fun_val);

end

% subroutine

function xp = proj(y)

% Projection of the vector y on to the nonnegative orthant

%

% INPUT

% ======================

% y ........a column vector

% OUTPUT

% ======================

% xp .......the orthogonal projection of y onto the nonnegative orthant

xp = max(y,0);

end

end