# New Three-Term Conjugate Gradient Method with Exact Line Search

Abstract

Conjugate Gradient (CG) methods have an important role in solving large scale unconstrained optimization problems. Nowadays, the Three-Term CG method has become a research trend of the CG methods. However, the existing Three-Term CG methods could only be used with the inexact line search. When the exact line search is 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 exact line search is proposed. This new Three-Term CG method satisfies the descent condition using the exact line search. Performance profile based on numerical results show that this proposed method outperforms the well-known classical CG method and some related hybrid methods. In addition, the proposed method is also robust in term of number of iterations and CPU time.