A hybridization of the Polak-Ribiere-Polyak and the Dai-Yuan conjugate gradient methods with sufficient descent property

Based on the convex combination of Polak-Ribiere-Polyak (PRP) and the Dai-Yuan (DY) conjugate gradient methods, we present a new hybrid conjugate gradient method for unconstrained optimization. In our method, the search directions of the proposed method satisfy the sufficient descent condition, independent of the accuracy of the line search. Under some standard assumptions, the global convergence property of the proposed method for general functions is established. We test our method on some test problems from CUTEst collection. Numerical results show efficiency and robustness of our proposed method in practice.