A New Hybrid PRP-MMR Conjugate Gradient Methods with Exact Line Search

Conjugate gradient (CG) methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new hybrid conjugate gradient method for solving unconstrained optimization problems, which is a convex combination of an earlier version of Polak- Ribiere and Polyak (PRP) and a recent modification of Mouiyad Bani Yousef (MMR) method. The proposed method is proved globally convergent under exact line search. This is supported by the results of the numerical tests. The numerical performance of the new hybrid CG method is reported to be more efficient compared with previous CG methods. Numerical experiments are made for two combinations of the new hybrid method and the PRP conjugate gradient method. The initial results show that one of the hybrid methods is especially effective for the given test problems.