Efficient one-parameter family of conjugate gradient methods

Abstract

We present an efficient one-parameter family of conjugate gradient methods for unconstrained optimization problems. These methods are defined using a combination of the Polak-Ribiere-Polyak method and the Rivaie-Mustafa-Ismail-Leong method. We prove the global convergence based on the Wolfe line search for nonlinear objective functions. Finally, we give some numerical experiments, proving the efficiency of the proposed approach.