An efficient modified Polak–Ribière–Polyak conjugate gradient method with global convergence properties. (2nd November 2017)

• Record Type: Journal Article
• Authors: Alhawarat, Ahmad; Salleh, Zabidin; Mamat, Mustafa; Rivaie, Mohd
• Is Part Of: Optimization methods and software. Volume 32:Number 6(2017)
• Page Start: 1299
• Page End: 1312
• Publication Date: 2017-11-02
• Subjects: conjugate gradient method -- inexact line search -- global convergence; 49m37 -- 65k05 -- 90c30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1266354
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : The conjugate gradient (CG) method is one of the most popular methods for solving large- scale unconstrained optimization problems. In this paper, a new modified version of the CG formula that was introduced by Polak, Ribière, and Polyak is proposed for problems that are bounded below and have a Lipschitz-continuous gradient. The new parameter provides global convergence properties when the strong Wolfe-Powell (SWP) line search or the weak Wolfe-Powell (WWP) line search is employed. A proof of a sufficient descent condition is provided for the SWP line search. Numerical comparisons between the proposed parameter and other recent CG modifications are made on a set of standard unconstrained optimization problems. The numerical results demonstrate the efficiency of the proposed CG parameter compared with the other CG parameters.