Another hybrid conjugate gradient method as a convex combination of NVHS∗ and CD methods

Abstract

Conjugate gradient methods play a fundamental role in solving unconstrained optimization problems. We propose a new hybrid conjugate gradient algorithm that forms a convex combination of βNVHS∗k and βCDk. The parameter θk is determined so as to satisfy the conjugacy condition. Under the strong Wolfe line search conditions, we establish both the descent property and the global convergence of the proposed hybrid method. Numerical experiments demonstrate that the new method is robust and computationally efficient.