Global Convergence Property with Inexact Line Search for a New Hybrid Conjugate Gradient Method

Abstract

In this study, we derive a new scale parameter φ for the CG method, for solving large scale unconstrained optimization algorithms. The new scale parameter φ satisfies the sufficient descent condition, global convergence analysis proved under Strong Wolfe line search conditions. Our numerical results show that the proposed method is effective and robust against some known algorithms.search, known as the line searches [2]. Among them, the so-called strong wolf line search conditions require that [3] [4].

A New Hybrid Conjugate Gradient Projection Method for Solving Nonlinear Monotone Equations

“…In [29], based on the MMWU method [30] and RMAR method [31], Fanar and Ghada proposed a new hybrid conjugate gradient method (HFG) as follows:…”

A new hybrid conjugate gradient algorithm for unconstrained optimization with inexact line search

“…We are going to prove that the sufficient descent condition holds for RMIL when inexact line search is used [22] they proved that the sufficient descent condition holds with exact line search. In [20], they proved that the sufficient descent condition holds with exact line search.…”

“…Many researchers devoted to the hybrid or mixed conjugate gradient methods which have better computational performances and strong convergence properties. Andrei [16] proposed the following hybrid method: ( ) ; Djordjevic' [17], proposed the following HCG method ( ) ; Xiuyun, et al [18], proposed the following HCG method ( ) ; Livieris, et al [19], proposed the following HCG method ( ) ; Al-Namat et al [20]. proposed the following HCG method ( ) .…”