HYBRID CONJUGATE GRADIENT METHOD UNDER EXACT AND INEXACT LINE SEARCH

Abstract

Hybridization is one of the frequent approaches in modifying the Conjugate Gradient (CG) method. In this paper, a new hybrid CG is introduced, and its performance is compared under two different line searches; exact and inexact line searches. The proposed hybrid CG is known as HSMR, is evaluated as a convex combination of RMIL and SMR methods. The comparisons were tested with twenty one different test functions under various dimensions. Both results are compared between number of iterations and total number of CPU time. The comparison performance showed that the hybrid CG is promising under exact line search compared to inexact line search in both of number of iterations and central CPU time.