A class of descent four–term extension of the Dai–Liao conjugate gradient method based on the scaled memoryless BFGS update

Saman Babaie–Kafaki; Reza Ghanbari

doi:10.3934/jimo.2016038

Article Contents

2017, Volume 13, Issue 2: 649-658. Doi: 10.3934/jimo.2016038

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A class of descent four–term extension of the Dai–Liao conjugate gradient method based on the scaled memoryless BFGS update

Saman Babaie–Kafaki^1, , and
Reza Ghanbari^2,

1.
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195–363, Semnan, Iran
2.
Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box: 9177948953, Mashhad, Iran

* Corresponding author: Saman Babaie–Kafaki
* Corresponding author: Saman Babaie–Kafaki

Received: November 2014

Revised: December 2015

Published: August 2017

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Abstract

Hybridizing the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Dai and Liao based on the scaled memoryless BFGS update, a one–parameter class of four–term conjugate gradient methods is proposed. It is shown that the suggested class of conjugate gradient methods possesses the sufficient descent property, without convexity assumption on the objective function. A brief global convergence analysis is made for uniformly convex objective functions. Results of numerical comparisons are reported. They demonstrate efficiency of a method of the proposed class in the sense of the Dolan–Moré performance profile.

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Mathematics Subject Classification: Primary: 65K05, 90C53; Secondary: 49M37.

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Figure 1. Total number of function and gradient evaluations performance profiles for NMDL1, NMDL2, NMDL3 and MDL

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Figure 2. CPU time performance profiles for NMDL1, NMDL2, NMDL3 and MDL

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