Linear search with simple back-tracking

function [y] = rosen(x)

% Rosenbrock function. Assume x is a 2-dimensional

% vector.

y = 100*(x(2)-x(1)^2)^2 + (1-x(1))^2 ;

function [Bnew] = bfgs(B,y,s)

% BFGS update

Bnew = B - (B*s*s'*B)/(s'*B*s) + y*y'/(y'*s) ;

function [Hnew] = dfp(H,y,s)

% DFP update

Hnew = H - (H*y*y'*H)/(y'*H*y) + s*s'/(y'*s) ;

function [g] = grad(x)

% gradient of rosenbrock function.

g = [-400*x(1)*(x(2)-x(1)^2)-2*(1-x(1)); 200*(x(2)-x(1)^2)] ;

function [H] = hessian(x)

% Hessian of rosenbrock function.

H = [1200*x(1)^2-400*x(2)+2, -400*x(1) ; -400*x(1), 200];

function [y] = linesearch(fun,x,d,g)

% Line-search along d with simple backtracking.

% Assume g = phi'(0) is also available.

alpha = 1 ;

c = 0.0001 ;

rho = 0.9 ;

while (feval(fun,x+alpha*d) > rosen(x) + c*alpha*g)

   alpha = rho*alpha ;

end ;

y = x+alpha*d ;