I'm getting an error in obtaining the optimal solution for a nonlinear equation

I'm trying to apply steepest descent satifying strong wolfe conditions to the Rosenbruck function with inital x0=(1.2,1.2), however, although the function itself has a unique solution at (1,1), I'm getting (-inf,inf) as an optimal solution. Here are the codes:

function [X,Grad,ite] = steepest_descent_wolfe(fhandle,x0,tol,maxit,alpha0,c,cu,mu,amax)
% Description:
% Obtains the iterations of a given function with given datas by using 
% steepest descent method with wolfe condition
%
% Input:
%      fhandle : objective function
%           x0 : initial guess
%          tol : tolerance
%        maxit : maximum number of iterations
%       alpha0 : initial step-length
%            c : Armijo parameter
%           cu : Strong curvature Parameter
%           mu : backtracking parameter
%         amax : maximum number of iteration for Wolfe contion
%
% Output:
%            X : solution containing each iteration
%         Grad : gradient of solution 
%          ite : number of iteration
% Usage:
%      steepest_descent_armijo(fhandle,x0,tol,maxit,alpha0,c,beta,amax)

ite = 1;

% Calculate function values at initial guess
[~,fgrad] = feval(fhandle,x0);

% Compute magnitude of gradient for stopping criteria
Grad(:,1) = norm(fgrad);

% Allocate initial point
x(:,1) = x0;

while( ite < maxit &&  norm(fgrad) > tol)
  
  % Compute the search direction
  p = -fgrad;
  
  % Compute step-length, satisfying Armijo condition
  alpha = wolfe(fhandle,x(:,ite),p,alpha0,c,cu,mu,amax);
  
  % Update the solution
  x(:,ite+1) = x(:,ite) + alpha*p;
  
  % Compute gradient of function at current point for stopping criteria
  [~,fgrad] = feval(fhandle,x(:,ite+1));
  
  % Compute magnitude of gradient for stopping criteria
  Grad(:,ite+1) = norm(fgrad);
    
  % Increase the iteration number
  ite = ite+1;
end

  X = x;
  
end

%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%
function alpha = wolfe(fhandle, x, p, alpha0, c, cu, mu, amax)

% Description:
%             Compute  step-length of an iteration satisfied by Wolfe condition
%
% Input:
%        fhandle : function handle
%              x : current point
%         alpha0 : initial step-length
%              c : Armijo parameter
%             cu : Curvature parameter
%             mu : backtracking parameter
%           amax : maximum number of iteration
%
% Output:
%        alpha: step-length of an iteration satisfied by Wolfe condition
%
% Usage:
%       wolfe(fhandle, x, p, alpha0, c, cu, mu, amax)

j = 0;

% Calculate function values at x
[f,gradx] = feval(fhandle,x);

% Calculate function values at x + alpha*p
[fh,gradk]   = feval(fhandle,x+alpha0*p);

while ( ( fh > f + c*alpha0*gradx'*p ) && ( j < amax ) && ( abs(gradk)'*p > cu*abs(gradx)'*p )) 
    
    % Update the step length by using backtracking with parameter mu
    alpha0 = alpha0*mu;
    
    % Update the iterate
    a  = x + alpha0*p;
    
    % Calculate function values at  x + alpha*p  
    [fh,gradk] = feval(fhandle,a);
    
    % Increase the iteration number
    j = j+1; 
    
end

alpha = alpha0;

end

%where the objective function is 
function [f,gradf] = rosenbrock(x)
f     = 100*(x(1)^2 - x(2))^2 + (x(1)-1)^2;
gradf = [100*(2*(x(1)^2-x(2))*2*x(1)) + 2*(x(1)-1); ...
         100*(-2*(x(1)^2-x(2))) ];

end
%%%the input values
x      = [1.2,1.2];   
tol    = 1.0e-4;      
maxit  = 100;      
alpha0 = 1;           
c      = 1.0e-4;     
cu     = 0.9;         
mu     = 0.5;         
amax   = 1000;   
%%%%%%%%

Answer 1

[Thiago Henrique Gomes Lobato]

You have an error in your wolf loop. It should be like this:

while ( ( ( fh > f + c*alpha0*gradx'*p ) || ( abs(gradk)'*p > cu*abs(gradx)'*p ) ) && ( j < amax )   ) 

Both conditions have to be fullfiled, if you use all && then only one of them is required. || and && can be indeed a little trickier in while loops. Replacing this in your code with your initial conditions I get:

X(:,end)

ans =

    1.1109
    1.2339

And, for maxit = 1000:

X(:,end)

ans =

    1.0046
    1.0093