A NEW ADAPTIVE SUBSPACE MINIMIZATION THREE-TERM CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

作     者：Keke Zhang Hongwei Liu Zexian Liu Keke Zhang;Hongwei Liu;Zexian Liu

作者机构：School of Mathematics and StatisticsXidian UniversityXi’an 710126China State Key Laboratory of Scientific and Engineering ComputingInstitute of Computational Mathematics and Scientific/Engineering computingAMSSChinese Academy of SciencesBeijing 100190China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2021年第39卷第2期

页      面：159-177页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：the editor and the anonymous referees for their valuable comments,which are helpful to improve the quality of this paper.We would like to thank Professor Dai Y.H.and Dr.Kou C.X.for their CGOPT code,and thank Professors Hager W.W.and Zhang H.C.for their CG_DESCENT(5.3)code This research is supported by National Science Foundation of China(No.11901561),China Postdoctoral Science Foundation(2019M660833) Guangxi Natural Science Foundation(No.2018GXNSFBA281180) 

主　　题：Conjugate gradient method Nonmonotone line search Subspace minimization Sufficient descent condition Global convergence 

摘      要：A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this *** search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces,and we also proposed an adaptive rule for choosing different searching directions at each *** obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent *** the used nonmonotone line search,we prove that the new algorithm is globally convergent for general nonlinear functions under some mild *** experiments show that the proposed algorithm is promising for the given test problem set.