KMS Of Academy of mathematics and systems sciences, CAS
A smoothing SQP framework for a class of composite minimization over polyhedron | |
Liu, Ya-Feng1; Ma, Shiqian2; Dai, Yu-Hong1; Zhang, Shuzhong3 | |
2016-07-01 | |
发表期刊 | MATHEMATICAL PROGRAMMING |
ISSN | 0025-5610 |
卷号 | 158期号:1-2页码:467-500 |
摘要 | The composite minimization problem over a general polyhedron has received various applications in machine learning, wireless communications, image restoration, signal reconstruction, etc. This paper aims to provide a theoretical study on this problem. First, we derive the Karush-Kuhn-Tucker (KKT) optimality conditions for local minimizers of the problem. Second, we propose a smoothing sequential quadratic programming framework for solving this problem. The framework requires a (approximate) solution of a convex quadratic program at each iteration. Finally, we analyze the worst-case iteration complexity of the framework for returning an -KKT point; i.e., a feasible point that satisfies a perturbed version of the derived KKT optimality conditions. To the best of our knowledge, the proposed framework is the first one with a worst-case iteration complexity guarantee for solving composite minimization over a general polyhedron. |
关键词 | Composite L-q minimization epsilon-KKT point Nonsmooth nonconvex non-Lipschitzian optimization Optimality condition Smoothing approximation Worst-case iteration complexity |
DOI | 10.1007/s10107-015-0939-5 |
语种 | 英语 |
资助项目 | NSFC[11331012] ; NSFC[11301516] ; NSFC[71331001] ; Hong Kong Research Grants Council General Research Fund Early Career Scheme[CUHK 439513] ; China National Funds for Distinguished Young Scientists Grant[11125107] ; Chinese National Programs for Fundamental Research and Development Grant[2015CB856000] ; CAS Program for Cross & Cooperative Team of the Science & Technology Innovation ; NSF[CMMI-1462408] |
WOS研究方向 | Computer Science ; Operations Research & Management Science ; Mathematics |
WOS类目 | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
WOS记录号 | WOS:000378003300016 |
出版者 | SPRINGER HEIDELBERG |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/22925 |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Liu, Ya-Feng |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China 3.Univ Minnesota, Dept Ind & Syst Engn, Minneapolis, MN 55455 USA |
推荐引用方式 GB/T 7714 | Liu, Ya-Feng,Ma, Shiqian,Dai, Yu-Hong,et al. A smoothing SQP framework for a class of composite minimization over polyhedron[J]. MATHEMATICAL PROGRAMMING,2016,158(1-2):467-500. |
APA | Liu, Ya-Feng,Ma, Shiqian,Dai, Yu-Hong,&Zhang, Shuzhong.(2016).A smoothing SQP framework for a class of composite minimization over polyhedron.MATHEMATICAL PROGRAMMING,158(1-2),467-500. |
MLA | Liu, Ya-Feng,et al."A smoothing SQP framework for a class of composite minimization over polyhedron".MATHEMATICAL PROGRAMMING 158.1-2(2016):467-500. |
条目包含的文件 | 条目无相关文件。 |
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