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

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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.

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Authors and Affiliations

  1. LMIB of the Ministry of Education, School of Mathematical Sciences, Beihang University, Beijing, 100191, People’s Republic of China

    Zhuoyi Xu, Yong Xia & Jiulin Wang

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  1. Zhuoyi Xu
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  2. Yong Xia
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  3. Jiulin Wang
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Correspondence to Jiulin Wang.

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This research was supported by National Natural Science Foundation of China under grants 11822103, 11571029, 11771056 and Beijing Natural Science Foundation Z180005.

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Xu, Z., Xia, Y. & Wang, J. Cheaper relaxation and better approximation for multi-ball constrained quadratic optimization and extension. J Glob Optim 80, 341–356 (2021). https://doi.org/10.1007/s10898-020-00985-x

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