An efficient adaptive three-term extension of the Hestenes–Stiefel conjugate gradient method. (4th May 2019)

• Record Type: Journal Article
• Authors: Dong, Xiao-Liang; Liu, Ze-Xian; Liu, Hong-Wei; Li, Xiang-Li
• Is Part Of: Optimization methods and software. Volume 34:Number 3(2019)
• Page Start: 546
• Page End: 559
• Publication Date: 2019-05-04
• Subjects: Unconstrained optimization -- conjugate gradient method -- conjugacy condition -- sufficient descent condition -- global convergence -- numerical comparison; 65K05 -- 90C53; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2017.1418870
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : A new three-term Hestenes–Stiefel-type conjugate gradient method is proposed in which the search direction can satisfy the sufficient descent condition as well as an adaptive conjugacy condition. It is notable that search directions of the method are dynamically adjusted between that of the Newton method and the 3HS+ method, accelerating the convergence or reducing the condition number of iteration matrix. Under mild conditions, we show that the proposed method converges globally for general objective functions. Numerical experiments indicate that the method is practically promising.