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.

Computation and Performance Analysis of Existing Three Term Conjugate Gradient Method

“…Reference [9] proposed a new three-term CG with exact line search using CG parameter of FR, HS and RMIL. The RMIL method which has been applied into the new proposed three term search direction is denoted as 3TNRMIL and performed better than FR and HS.…”