Global optimization in Hilbert space
2019-01
Source PublicationMATHEMATICAL PROGRAMMING
ISSN0025-5610
Volume173Issue:1-2Pages:221-249
Status已发表
DOI10.1007/s10107-017-1215-7
AbstractWe propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an epsilon-suboptimal global solution within finite run-time for any given termination tolerance epsilon>0. Finally, we illustrate these results for a problem of calculus of variations.
KeywordInfinite-dimensional optimization Complete search Branch-and-lift Convergence analysis Complexity analysis
Indexed BySCI ; SCIE ; EI
Language英语
Funding ProjectMarie Curie Career Integration Grant[PCIG09-GA-2011-293953]
WOS Research AreaComputer Science ; Operations Research & Management Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000456970900007
PublisherSPRINGER HEIDELBERG
WOS KeywordCONVEX COMPUTATION ; APPROXIMATIONS ; INTERSECTION ; INTEGRATION ; ELLIPSOIDS ; ALGORITHM ; CUT ; SET
Original Document TypeArticle
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Document Type期刊论文
Identifierhttps://kms.shanghaitech.edu.cn/handle/2MSLDSTB/29712
Collection信息科学与技术学院_PI研究组_Boris Houska组
Corresponding AuthorChachuat, Benoit
Affiliation
1.ShanghaiTech Univ, Sch Informat Sci & Technol, 319 Yueyang Rd, Shanghai 200031, Peoples R China
2.Imperial Coll London, Ctr Proc Syst Engn, Dept Chem Engn, South Kensington Campus, London SW7 2AZ, England
First Author AffilicationSchool of Information Science and Technology
First Signature AffilicationSchool of Information Science and Technology
Recommended Citation
GB/T 7714
Houska, Boris,Chachuat, Benoit. Global optimization in Hilbert space[J]. MATHEMATICAL PROGRAMMING,2019,173(1-2):221-249.
APA Houska, Boris,&Chachuat, Benoit.(2019).Global optimization in Hilbert space.MATHEMATICAL PROGRAMMING,173(1-2),221-249.
MLA Houska, Boris,et al."Global optimization in Hilbert space".MATHEMATICAL PROGRAMMING 173.1-2(2019):221-249.
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