A Modified Nonmonotone Hestenes–Stiefel Type Conjugate Gradient Methods for Large-Scale Unconstrained Problems. (2nd January 2017)

• Record Type: Journal Article
• Authors: Dong, Xiao-Liang; Liu, Hong-Wei; Li, Xiang-Li; He, Yu-Bo; Liu, Ze-Xian
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 1(2017)
• Page Start: 39
• Page End: 50
• Publication Date: 2017-01-02
• Subjects: Conjugate gradient method -- global convergence -- sufficient descent condition -- numerical comparison; 90C30 -- 90C06 -- 90C52 -- 90C53; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1232730
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, by slightly modifying the search direction of the nonmonotone Hestenes–Stiefel method, a variant Hestenes–Stiefel conjugate gradient method is proposed that satisfies the sufficient descent condition independent of any line search. This algorithm also possesses information about the gradient value and the function value. We establish the global convergence of our methods without the assumption that the steplength is bounded away from zero. Numerical results illustrate that our method can efficiently solve the test problems, and therefore is promising.