New hybrid BFGS-CG method for solving unconstrained optimization

Abstract

Conjugate gradient method and quasi-Newton (QN) method are both well known solvers for solving unconstrained optimization problems. In this paper, we proposed a new conjugate gradient method denoted as Wan, Asrul and Mustafa (WAM) method. This WAM method is then combined with the QN method to produce a new hybrid search direction which is QN-WAM. Based on numerical results, the proposed hybrid method proved to be more efficient compared to the original quasi-Newton method and other hybrid methods.