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
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| 2016-07-01 | |
| Source Publication | MATHEMATICAL PROGRAMMING
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| ISSN | 0025-5610 |
| Volume | 158Issue:1-2Pages:467-500 |
| Abstract | 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. |
| Keyword | 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 |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
| WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000378003300016 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/22925 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Liu, Ya-Feng |
| Affiliation | 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 |
| Recommended Citation 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. |
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