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Stochastic proximal quasi-Newton methods for non-convex composite optimization

文献类型：期刊论文

作者Wang, Xiaoyu1,2; Wang, Xiao1; Yuan, Ya-xiang2
刊名OPTIMIZATION METHODS & SOFTWARE
出版日期2019-09-03
卷号34期号:5页码:922-948
关键词Non-convex composite optimization Polyak-Lojasiewicz (PL) inequality stochastic gradient stochastic variance reduction gradient symmetric rank one method rank one proximity operator complexity bound
ISSN号1055-6788
DOI10.1080/10556788.2018.1471141
英文摘要In this paper, we propose a generic algorithmic framework for stochastic proximal quasi-Newton (SPQN) methods to solve non-convex composite optimization problems. Stochastic second-order information is explored to construct proximal subproblem. Under mild conditions we show the non-asympotic convergence of the proposed algorithm to stationary point of original problems and analyse its computational complexity. Besides, we extend the proximal form of Polyak-Lojasiewicz (PL) inequality to constrained settings and obtain the constrained proximal PL (CP-PL) inequality. Under CP-PL inequality linear convergence rate of the proposed algorithm is achieved. Moreover, we propose a modified self-scaling symmetric rank one incorporated in the framework for SPQN method, which is called stochastic symmetric rank one method. Finally, we report some numerical experiments to reveal the effectiveness of the proposed algorithm.
资助项目National Natural Science Foundation of China[11331012] ; National Natural Science Foundation of China[11301505] ; National Natural Science Foundation of China[11731013] ; National Natural Science Foundation of China[11688101]
WOS研究方向Computer Science ; Operations Research & Management Science ; Mathematics
语种英语
WOS记录号WOS:000486079100002
出版者TAYLOR & FRANCIS LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/35631]  
专题中国科学院数学与系统科学研究院
通讯作者Wang, Xiao
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
2.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, AMSS, Beijing, Peoples R China
推荐引用方式
GB/T 7714		 Wang, Xiaoyu,Wang, Xiao,Yuan, Ya-xiang. Stochastic proximal quasi-Newton methods for non-convex composite optimization[J]. OPTIMIZATION METHODS & SOFTWARE,2019,34(5):922-948.
APA Wang, Xiaoyu,Wang, Xiao,&Yuan, Ya-xiang.(2019).Stochastic proximal quasi-Newton methods for non-convex composite optimization.OPTIMIZATION METHODS & SOFTWARE,34(5),922-948.
MLA Wang, Xiaoyu,et al."Stochastic proximal quasi-Newton methods for non-convex composite optimization".OPTIMIZATION METHODS & SOFTWARE 34.5(2019):922-948.

入库方式： OAI收割

来源：数学与系统科学研究院

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