Chebyshev center of the intersection of balls: complexity, relaxation and approximation
文献类型：期刊论文
| 作者 | Xia, Yong2; Yang, Meijia2; Wang, Shu1 |
| 刊名 | MATHEMATICAL PROGRAMMING
 |
| 出版日期 | 2020-02-17 |
| 页码 | 29 |
| ISSN号 | 0025-5610 |
| 关键词 | Chebyshev center Minimax Nonconvex quadratic optimization Semidefinite programming Strong duality Linear programming Approximation Complexity |
| DOI | 10.1007/s10107-020-01479-0 |
| 英文摘要 | We 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. |
| 资助项目 | National 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研究方向 | Computer Science ; Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| 出版者 | SPRINGER HEIDELBERG |
| WOS记录号 | WOS:000516414600002 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50889]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Wang, Shu |
| 作者单位 | 1.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.Beihang Univ, Sch Math & Syst Sci, Minist Educ, LMIB, Beijing 100191, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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