New Three-Term Conjugate Gradient Method with Exact Line Search

Abstract

Conjugate Gradient (CG) methods have an important role in solving largescale unconstrained optimization problems. Nowadays, the Three-Term CG method hasbecome a research trend of the CG methods. However, the existing Three-Term CGmethods could only be used with the inexact line search. When the exact line searchis applied, this Three-Term CG method will be reduced to the standard CG method.Hence in this paper, a new Three-Term CG method that could be used with the exactline search is proposed. This new Three-Term CG method satisfies the descent conditionusing the exact line search. Performance profile based on numerical results show thatthis proposed method outperforms the well-known classical CG method and some relatedhybrid methods. In addition, the proposed method is also robust in term of number ofiterations and CPU time.