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FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS
Wang, Shuxiong; Yuan, Yaxiang
2015
Source PublicationSIAM JOURNAL ON OPTIMIZATION
ISSN1052-6234
Volume25Issue:4Pages:2537-2560
AbstractA new numerical method is presented for semi-infinite optimization problems which guarantees that each iterate is feasible for the original problem. The basic idea is to construct concave relaxations of the lower level problem, to compute the optimal values of the relaxation problems explicitly, and to solve the resulting approximate problems with finitely many constraints. The concave relaxations are constructed by replacing the objective function of the lower level problem by its concave upper bound functions. Under mild conditions, we prove that every accumulation point of the solutions of the approximate problems is an optimal solution of the original problem. An adaptive subdivision algorithm is proposed to solve semi-infinite optimization problems. It is shown that the Karush-Kuhn-Tucker points of the approximate problems converge to a Karush-Kuhn-Tucker point of the original problem within arbitrarily given tolerances. Numerical experiments show that our algorithm is much faster than the existing adaptive convexification algorithm in computation time.
Keywordsemi-infinite programs concave optimization adaptive subdivision algorithm
DOI10.1137/140982143
Language英语
Funding ProjectNSFC[11331012] ; NSFC[11321061] ; NSFC[11461161005]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000367019700023
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21591
Collection计算数学与科学工程计算研究所
Corresponding AuthorWang, Shuxiong
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Wang, Shuxiong,Yuan, Yaxiang. FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS[J]. SIAM JOURNAL ON OPTIMIZATION,2015,25(4):2537-2560.
APA Wang, Shuxiong,&Yuan, Yaxiang.(2015).FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS.SIAM JOURNAL ON OPTIMIZATION,25(4),2537-2560.
MLA Wang, Shuxiong,et al."FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS".SIAM JOURNAL ON OPTIMIZATION 25.4(2015):2537-2560.
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