A class of globally convergent conjugate gradient methods

Abstract

Conjugate gradient methods are very important ones for solving nonlinear optimization problems, especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods were usually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can be regarded as some kind of convex combination of the Fletcher-Reeves method and the method proposed by Dai et al. To analyze this class of methods, we introduce some unified tools that concern a general method with the scalar βk having the form of φk/ φk−1.Consequently, the class of conjugate gradient methods can uniformly be analyzed.