Two new spectral conjugate gradient algorithms based on Hestenes–Stiefel. Issue 4 (December 2017)

• Record Type: Journal Article
• Authors: Wang, Guofang; Shan, Rui; Huang, Wei; Liu, Wen; Zhao, Jingyi
• Is Part Of: Journal of algorithms & computational technology. Volume 11:Issue 4(2017)
• Page Start: 345
• Page End: 352
• Publication Date: 2017-12
• Subjects: Spectral conjugate gradient algorithm -- unconstrained optimization -- Wolfe line search -- sufficient descent property -- globally convergent; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748301817725296
• Languages: English
• ISSNs: 1748-3018

Abstract

The spectral conjugate gradient algorithm, which is a variant of conjugate gradient method, is one of the effective methods for solving unconstrained optimization problems. In this paper, based on Hestenes–Stiefel method, two new spectral conjugate gradient algorithms (Descend Hestenes-Stiefel (DHS) and Wang-Hestenes-Stiefel (WHS)) are proposed. Under Wolfe line search and mild assumptions on objective function, the two algorithms possess sufficient descent property without any other conditions and are always globally convergent. Numerical results turn out the new algorithms outperform Hestenes–Stiefel conjugate gradient method.