Cheaper relaxation and better approximation for multi-ball constrained quadratic optimization and extension

Zhuoyi Xu (), Yong Xia () and Jiulin Wang ()
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Zhuoyi Xu: Beihang University
Yong Xia: Beihang University
Jiulin Wang: Beihang University

Journal of Global Optimization, 2021, vol. 80, issue 2, No 5, 356 pages

Abstract: Abstract We propose a convex quadratic programming (CQP) relaxation for multi-ball constrained quadratic optimization (MB). (CQP) is shown to be equivalent to semidefinite programming relaxation in the hard case. Based on (CQP), we propose an algorithm for solving (MB), which returns a solution of (MB) with an approximation bound independent of the number of constraints. The approximation algorithm is further extended to solve nonconvex quadratic optimization with more general constraints. As an application, we propose a standard quadratic programming relaxation for finding Chebyshev center of a general convex set with a guaranteed approximation bound.

Keywords: Quadratic optimization; Semidefinite programming; Approximation algorithm; Chebyshev center; 90C20; 90C22; 90C30; 90C59 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-020-00985-x

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