Global Convergence of Conjugate Gradient Methods without Line Search

作     者：Cuiling CHEN Yu CHEN 

作者机构：College of Mathematics and Statistics Guangxi Normal University School of Computing and Information University of Pittsburgh 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))

年 卷 期：2018年第38卷第5期

页      面：541-550页

核心收录：

学科分类：07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11761014) the Natural Science Foundation of Guangxi Zhuang Autonomous Region(Grant No.2017GXNSFAA198243) Guangxi Basic Ability Improvement Project for the Middle-Aged and Young Teachers of Colleges and Universities(Grant Nos.2017KY0068 KY2016YB069) Guangxi Higher Education Undergraduate Course Teaching Reform Project(Grant No.2017JGB147) 

主　　题：unconstrained optimization conjugate gradient method line search global convergence 

摘      要：In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows:（1） The DY method globally converges for a strongly convex LC;objective function;（2） The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC;objective function.