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AN OUTER APPROXIMATION METHOD FOR A CLASS OF MINIMAX CONVEX MINLP PROBLEMS
Chen, Liang1,2; Dai, Yu-Hong1,2; Wei, Zhou3
2019
Source PublicationJOURNAL OF NONLINEAR AND CONVEX ANALYSIS
ISSN1345-4773
Volume20Issue:3Pages:379-393
AbstractIn this paper, we mainly study a class of mixed-integer nonlinear program (MINLP) problems whose objective and constraint functions are the maximum of finite convex smooth functions. Such problems refer to the combination of two areas of MINLP and nonsmooth optimization. For solving these minimax convex MINLP problems, we consider an outer approximation method and use KKT optimality conditions and subgradients to reformulate MINLP as an equivalent mixed-integer linear program (MILP). Then we construct an outer approximation algorithm for solving a sequence of relaxed MILP problems so as to find the optimal solution of MINLP. The algorithm is proved to terminate after a finite number of steps. To illustrate the feasibility of the outer approximation method for such problems, several minimax convex MINLP examples are provided and calculated by this algorithm. All computational tests are implemented by MILP solvers of Matlab and BARON.
KeywordMinimax convex problem MINLP outer approximation subgradient master program
Language英语
Funding ProjectChinese Natural Science Foundation[11631013] ; Chinese Natural Science Foundation[71331001] ; Chinese Natural Science Foundation[11331012] ; Chinese Natural Science Foundation[11826204] ; National 973 Program of China[2015CB856002] ; National Natural Science Foundations of China[11826206] ; National Natural Science Foundations of China[11771384] ; Natural Science Foundation of Yunnan Province of China[2018FB004] ; Scientific Research Foundation of Yunnan University[2018YDJQ010] ; Yunnan Provincial Science and Technology Department[2018FY001(-014)] ; IRTSTYN ; Yunnan University[2018FY001(-014)]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000467670700002
PublisherYOKOHAMA PUBL
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34760
Collection计算数学与科学工程计算研究所
Corresponding AuthorWei, Zhou
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Yunnan Univ, Dept Math, Kunming 650091, Yunnan, Peoples R China
Recommended Citation
GB/T 7714
Chen, Liang,Dai, Yu-Hong,Wei, Zhou. AN OUTER APPROXIMATION METHOD FOR A CLASS OF MINIMAX CONVEX MINLP PROBLEMS[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS,2019,20(3):379-393.
APA Chen, Liang,Dai, Yu-Hong,&Wei, Zhou.(2019).AN OUTER APPROXIMATION METHOD FOR A CLASS OF MINIMAX CONVEX MINLP PROBLEMS.JOURNAL OF NONLINEAR AND CONVEX ANALYSIS,20(3),379-393.
MLA Chen, Liang,et al."AN OUTER APPROXIMATION METHOD FOR A CLASS OF MINIMAX CONVEX MINLP PROBLEMS".JOURNAL OF NONLINEAR AND CONVEX ANALYSIS 20.3(2019):379-393.
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