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Chebyshev center of the intersection of balls: complexity, relaxation and approximation
Xia, Yong1; Yang, Meijia1; Wang, Shu2
2020-02-17
Source PublicationMATHEMATICAL PROGRAMMING
ISSN0025-5610
Pages29
AbstractWe study the n-dimensional problem of finding the smallest ball enclosing the intersection of p given balls, the so-called Chebyshev center problem (CCB). It is a minimax optimization problem and the inner maximization is a uniform quadratic optimization problem (UQ). When p = n, (UQ) is known to enjoy a strong duality and consequently (CCB) is solved via a standard convex quadratic programming (SQP). In this paper, we first prove that (CCB) is NP-hard and the special case when n = 2 is polynomially solvable. With the help of a newly introduced linear programming relaxation (LP), the (SQP) relaxation is reobtained more directly and the first approximation bound for the solution obtained by (SQP) is established for the hard case p > n. Finally, also based on (LP), we showthat (CCB) is polynomially solvablewhen either n or p-n(> 0) is fixed.
KeywordChebyshev center Minimax Nonconvex quadratic optimization Semidefinite programming Strong duality Linear programming Approximation Complexity
DOI10.1007/s10107-020-01479-0
Indexed BySCI
Language英语
Funding ProjectNational Science Fund for Excellent Young Scholars[11822103] ; National Natural Science Foundation of China[11801173] ; National Natural Science Foundation of China[11571029] ; National Natural Science Foundation of China[11771056] ; Beijing Natural Science Foundation[Z180005]
WOS Research AreaComputer Science ; Operations Research & Management Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000516414600002
PublisherSPRINGER HEIDELBERG
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50890
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWang, Shu
Affiliation1.Beihang Univ, Sch Math & Syst Sci, Minist Educ, LMIB, Beijing 100191, Peoples R China
2.Chinese 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
Xia, Yong,Yang, Meijia,Wang, Shu. Chebyshev center of the intersection of balls: complexity, relaxation and approximation[J]. MATHEMATICAL PROGRAMMING,2020:29.
APA Xia, Yong,Yang, Meijia,&Wang, Shu.(2020).Chebyshev center of the intersection of balls: complexity, relaxation and approximation.MATHEMATICAL PROGRAMMING,29.
MLA Xia, Yong,et al."Chebyshev center of the intersection of balls: complexity, relaxation and approximation".MATHEMATICAL PROGRAMMING (2020):29.
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