Hi
This is a long story, I make it short:
I am working in a project where I need to find a matrix defined by a third degree polynomial, the solution can be found iteratively using a gradient descent technique, I am using the golden section line search already implemented in matlab (with the code described below).
The algorithm looks powerful (it finds automatically the perfect step), but  unfortunately the golden section line search does not avoid being stuck in local minima. How can I implement more efficiently this. The problem is that sometime it converges and sometimes no (sometimes is not science :-).

%Initial third degree polynomial
Cest = initial_guess;
normdev=inf ;
stepsize=inf;

%Stopping condition
stopping_condition = 10^(-5) * norm(X*X'/no_samples,'fro');
 
while abs(normdev*stepsize) > stopping_condition
%Third degree polynomial  
dnew = Cest - 1/no_samples*(X*X' - 2/sigma^2 * (Cest*Cest'*Cest-Cest*B'*Cest));
  %Find the best stepsize as a minimum using the goldensection line search
    stepsize = fminbnd( @(stepsize)   step(stepsize,Cest,dnew,X*X',B,sigma,no_samples),-.1,.1);

    %Update 
     Cest = Cest + stepsize*dnew;
     normdev = norm(dnew,'fro');
end

function error = step(stepsize,Cest,dnew,XX,B,sigma,no_samples)
Cest = Cest + stepsize*dnew;
error = norm(Cest - 1/no_samples*(XX - 2/sigma^2 * (Cest^3-Cest*B*Cest)),'fro');

I tried :
  %Quasi-Newton
   stepsize = fminunc( @(stepsize) step(stepsize,Cest,dnew,X*X',B,sigma,no_samples),dnew);
But matlab get stuck (no heap memory) probably due the fact that this function is suppose to be used when we don't have a trust region.

Any suggestions ?