KMS Of Academy of mathematics and systems sciences, CAS
| Stochastic proximal quasi-Newton methods for non-convex composite optimization | |
| Wang, Xiaoyu1,2; Wang, Xiao2; Yuan, Ya-xiang1 | |
| 2019-09-03 | |
| Source Publication | OPTIMIZATION METHODS & SOFTWARE
 |
| ISSN | 1055-6788 |
| Volume | 34Issue:5Pages:922-948 |
| Abstract | 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. |
| Keyword | Non-convex composite optimization Polyak-Lojasiewicz (PL) inequality stochastic gradient stochastic variance reduction gradient symmetric rank one method rank one proximity operator complexity bound |
| DOI | 10.1080/10556788.2018.1471141 |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
| WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000486079100002 |
| Publisher | TAYLOR & FRANCIS LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35632 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wang, Xiao |
| Affiliation | 1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, AMSS, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China |
| Recommended Citation 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. |
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