Least-squares-based three-term conjugate gradient methods

Journal of inequalities and applications

article

Chunming Tang¹  Shuangyu Li¹  Zengru Cui¹ 

[1] College of Mathematics and Information Science, Guangxi University

关键词: Three-term conjugate gradient method;    Least-squares technique;    Sufficient descent property;    Wolfe–Powell line search;    Global convergence;   

DOI  :  10.1186/s13660-020-2301-6

学科分类：电力

来源: SpringerOpen

【 摘 要 】

In this paper, we first propose a new three-term conjugate gradient (CG) method, which is based on the least-squares technique, to determine the CG parameter, named LSTT. And then, we present two improved variants of the LSTT CG method, aiming to obtain the global convergence property for general nonlinear functions. The least-squares technique used here well combines the advantages of two existing efficient CG methods. The search directions produced by the proposed three methods are sufficient descent directions independent of any line search procedure. Moreover, with the Wolfe–Powell line search, LSTT is proved to be globally convergent for uniformly convex functions, and the two improved variants are globally convergent for general nonlinear functions. Preliminary numerical results are reported to illustrate that our methods are efficient and have advantages over two famous three-term CG methods.

【 授权许可】

CC BY