A modified Hestenes–Stiefel conjugate gradient method with an optimal property. (4th July 2019)

• Record Type: Journal Article
• Authors: Amini, Keyvan; Faramarzi, Parvaneh; Pirfalah, Nasrin
• Is Part Of: Optimization methods and software. Volume 34:Number 4(2019)
• Page Start: 770
• Page End: 782
• Publication Date: 2019-07-04
• Subjects: unconstrained optimization -- conjugate gradient method -- sufficient descent condition -- global convergence; 65K05 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1457150
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, based on the numerical efficiency of Hestenes–Stiefel (HS) method, a new modified HS algorithm is proposed for unconstrained optimization. The new direction independent of the line search satisfies in the sufficient descent condition. Motivated by theoretical and numerical features of three-term conjugate gradient (CG) methods proposed by Narushima et al., similar to Dai and Kou approach, the new direction is computed by minimizing the distance between the CG direction and the direction of the three-term CG methods proposed by Narushima et al. Under some mild conditions, we establish global convergence of the new method for general functions when the standard Wolfe line search is used. Numerical experiments on some test problems from the CUTEst collection are given to show the efficiency of the proposed method.