Chebyshev Center of the Intersection of Balls: Complexity, Relaxation and Approximation

Autor:	Xia, Yong, Yang, Meijia, Wang, Shu
Rok vydání:	2019
Předmět:	Mathematics - Optimization and Control 90C47 90C26 90C20
Druh dokumentu:	Working Paper
Popis:	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 strongly polynomially solved. 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 show that (CCB) is polynomially solved when either n or p-n(> 0) is fixed. Comment: 26 pages, 0 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1901.07645 Zobrazit plný text záznamu View this record from Arxiv