A class of smooth exact penalty function methods for optimization problems with orthogonality constraints
文献类型：期刊论文
| 作者 | Xiao, Nachuan1,2; Liu, Xin1,2; Yuan, Ya-xiang1 |
| 刊名 | OPTIMIZATION METHODS & SOFTWARE
 |
| 出版日期 | 2020-11-25 |
| 页码 | 37 |
| 关键词 | Orthogonality constraint Stiefel manifold augmented Lagrangian method |
| ISSN号 | 1055-6788 |
| DOI | 10.1080/10556788.2020.1852236 |
| 英文摘要 | Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose a novel penalty function with compact convex constraints (PenC). We show that PenC can act as an exact penalty model which shares the same global minimizers as the original problem with orthogonality constraints. Based on PenC, we first propose a first-order algorithm called PenCF and establish its global convergence and local linear convergence rate under some mild assumptions. For the case that the computation and storage of Hessian is achievable, and we pursue high precision solution and fast local convergence rate, a second-order approach called PenCS is proposed for solving PenC. To avoid expensive calculation or solving a hard subproblem in computing the Newton step, we propose a new strategy to do it approximately which still leads to quadratic convergence locally. Moreover, the main iterations of both PenCF and PenCS are orthonormalization-free and hence parallelizable. Numerical experiments illustrate that PenCF is comparable with the existing first-order methods. Furthermore, PenCS shows its stability and high efficiency in obtaining high precision solution comparing with the existing second-order methods. |
| 资助项目 | National Natural Science Foundation of China[11971466] ; National Natural Science Foundation of China[11991021] ; National Natural Science Foundation of China[11991020] ; Key Research Program of Frontier Sciences, Chinese Academy of Sciences[ZDBS-LY-7022] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences ; Youth Innovation Promotion Association, Chinese Academy of Sciences ; NSFC[11688101] |
| WOS研究方向 | Computer Science ; Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000592046900001 |
| 出版者 | TAYLOR & FRANCIS LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52482]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Liu, Xin |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xiao, Nachuan,Liu, Xin,Yuan, Ya-xiang. A class of smooth exact penalty function methods for optimization problems with orthogonality constraints[J]. OPTIMIZATION METHODS & SOFTWARE,2020:37. |
| APA | Xiao, Nachuan,Liu, Xin,&Yuan, Ya-xiang.(2020).A class of smooth exact penalty function methods for optimization problems with orthogonality constraints.OPTIMIZATION METHODS & SOFTWARE,37. |
| MLA | Xiao, Nachuan,et al."A class of smooth exact penalty function methods for optimization problems with orthogonality constraints".OPTIMIZATION METHODS & SOFTWARE (2020):37. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。