Some new three-term Hestenes–Stiefel conjugate gradient methods with affine combination. (4th May 2017)

• Record Type: Journal Article
• Authors: Dong, Xiao-Liang; Han, De-Ren; Ghanbari, Reza; Li, Xiang-Li; Dai, Zhi-Feng
• Is Part Of: Optimization. Volume 66:Number 5(2017)
• Page Start: 759
• Page End: 776
• Publication Date: 2017-05-04
• Subjects: Three-term conjugate gradient method -- sufficient descent condition -- quasi-Newton condition -- global convergence -- affine combination; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1295242
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, a modified Hestenes–Stiefel conjugate gradient method for unconstrained problems is developed, which can achieves the twin goals of generating sufficient descent direction at each iteration as well as being close to the Newton direction. In our methods, the hybridization parameter can also be obtained based on other kinds of conjugacy conditions. Under mild condition, we establish their global convergence for general objective functions. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.