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

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  • Zhuoyi Xu

    (Beihang University)

  • Yong Xia

    (Beihang University)

  • Jiulin Wang

    (Beihang University)

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.

Suggested Citation

  • Zhuoyi Xu & Yong Xia & Jiulin Wang, 2021. "Cheaper relaxation and better approximation for multi-ball constrained quadratic optimization and extension," Journal of Global Optimization, Springer, vol. 80(2), pages 341-356, June.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:2:d:10.1007_s10898-020-00985-x
    DOI: 10.1007/s10898-020-00985-x
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    References listed on IDEAS

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    1. Minyue Fu & Zhi-Quan Luo & Yinyu Ye, 1998. "Approximation Algorithms for Quadratic Programming," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 29-50, March.
    2. NESTEROV, Yu., 1998. "Semidefinite relaxation and nonconvex quadratic optimization," LIDAM Reprints CORE 1362, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Flippo, Olaf E. & Jansen, Benjamin, 1996. "Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid," European Journal of Operational Research, Elsevier, vol. 94(1), pages 167-178, October.
    4. A. Beck, 2009. "Convexity Properties Associated with Nonconvex Quadratic Matrix Functions and Applications to Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 1-29, July.
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