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A smoothing SQP framework for a class of composite minimization over polyhedron
Liu, Ya-Feng1; Ma, Shiqian2; Dai, Yu-Hong1; Zhang, Shuzhong3
AbstractThe 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.
KeywordComposite L-q minimization epsilon-KKT point Nonsmooth nonconvex non-Lipschitzian optimization Optimality condition Smoothing approximation Worst-case iteration complexity
Funding ProjectNSFC[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 AreaComputer Science ; Operations Research & Management Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000378003300016
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Document Type期刊论文
Corresponding AuthorLiu, Ya-Feng
Affiliation1.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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