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

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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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 (2021). https://doi.org/10.1007/s10898-020-00985-x

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Keywords

  • Quadratic optimization
  • Semidefinite programming
  • Approximation algorithm
  • Chebyshev center

Mathematics Subject Classification

  • 90C20
  • 90C22
  • 90C30
  • 90C59