An Optimal Extension of the Polak–Ribière–Polyak Conjugate Gradient Method. (2nd September 2017)

• Record Type: Journal Article
• Authors: Babaie–Kafaki, Saman; Ghanbari, Reza
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 9(2017)
• Page Start: 1115
• Page End: 1124
• Publication Date: 2017-09-02
• Subjects: Conjugate gradient method -- global convergence -- large-scale optimization -- singular value -- unconstrained optimization; 90C53 -- 49M37 -- 65K05 -- 65F35; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1320673
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Based on a singular value analysis on an extension of the Polak–Ribière–Polyak method, a nonlinear conjugate gradient method with the following two optimal features is proposed: the condition number of its search direction matrix is minimum and also, the distance of its search direction from the search direction of a descent nonlinear conjugate gradient method proposed by Zhang et al. is minimum. Under proper conditions, global convergence of the method can be achieved. To enhance efficiency of the proposed method, Powell's truncation of the conjugate gradient parameters is used. The method is computationally compared with the nonlinear conjugate gradient method proposed by Zhang et al. and a modified Polak–Ribière–Polyak method proposed by Yuan. Results of numerical comparisons show efficiency of the proposed method in the sense of the Dolan–Moré performance profile.