A globally convergent gradient-like method based on the Armijo line search

In this paper,  a new conjugate gradient-like algorithm is proposed to solve unconstrained optimization problems. The step directions generated by the new algorithm satisfy sufficient descent condition independent of the line search. The global convergence of the new algorithm, with the Armijo backtracking line search,  is proved.  Numerical experiments indicate the efficiency and robustness of the new algorithm.

Keywords:

Unconstrained optimization , conjugate gradient algorithm , Global convergence , Armijo condition