A spectral conjugate gradient method for solving large-scale unconstrained optimization

Abstract

This paper establishes a spectral conjugate gradient method for solving unconstrained optimization problems, where the conjugate parameter and the spectral parameter satisfy a restrictive relationship. The search direction is sufficient descent without restarts in per-iteration. Moreover, this feature is independent of any line searches. Under the standard Wolfe line searches, the global convergence of the proposed method is proved when |βk|≤βkFR holds. The preliminary numerical results are presented to show effectiveness of the proposed method.