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A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints

Author

Listed:
  • Zhuoyi Xu

    (Capital University of Economics and Business)

  • Linbin Li

    (Beihang University)

  • Yong Xia

    (Beihang University)

Abstract

An efficient partial ellipsoid approximation scheme is presented to find a $$\frac{1}{\lceil {\frac{m}{2}}\rceil }$$ 1 ⌈ m 2 ⌉ -approximation solution to the nonconvex homogeneous quadratic optimization with m convex quadratic constraints, where $$\lceil x \rceil $$ ⌈ x ⌉ is the smallest integer larger than or equal to x. If there is an additional nonconvex quadratic constraint beyond the m convex constraints, we can use the new scheme to find a $$\frac{1}{m}$$ 1 m -approximation solution.

Suggested Citation

  • Zhuoyi Xu & Linbin Li & Yong Xia, 2023. "A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 93-109, August.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:1:d:10.1007_s00186-023-00827-y
    DOI: 10.1007/s00186-023-00827-y
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    References listed on IDEAS

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    1. D. Henrion & S. Tarbouriech & D. Arzelier, 2001. "LMI Approximations for the Radius of the Intersection of Ellipsoids: Survey," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 1-28, January.
    2. 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.
    3. B. T. Polyak, 1998. "Convexity of Quadratic Transformations and Its Use in Control and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 553-583, December.
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