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Approximation Bounds for Trilinear and Biquadratic Optimization Problems Over Nonconvex Constraints

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  • Yuning Yang

    (Nankai University)

  • Qingzhi Yang

    (Nankai University)

  • Liqun Qi

    (The Hong Kong Polytechnic University)

Abstract

This paper presents new approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints. We first consider the partial semidefinite relaxation of the original problem, and show that there is a bounded approximation solution to it. This will be achieved by determining the diameters of certain convex bodies. We then show that there is also a bounded approximation solution to the original problem via extracting the approximation solution of its semidefinite relaxation. Under some conditions, the approximation bounds obtained in this paper improve those in the literature.

Suggested Citation

  • Yuning Yang & Qingzhi Yang & Liqun Qi, 2014. "Approximation Bounds for Trilinear and Biquadratic Optimization Problems Over Nonconvex Constraints," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 841-858, December.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:3:d:10.1007_s10957-014-0538-2
    DOI: 10.1007/s10957-014-0538-2
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    References listed on IDEAS

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    1. Xinzhen Zhang & Chen Ling & Liqun Qi, 2011. "Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints," Journal of Global Optimization, Springer, vol. 49(2), pages 293-311, February.
    2. Sheng-Long Hu & Zheng-Hai Huang, 2011. "Alternating direction method for bi-quadratic programming," Journal of Global Optimization, Springer, vol. 51(3), pages 429-446, November.
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    Cited by:

    1. Shigui Li & Linzhang Lu & Xing Qiu & Zhen Chen & Delu Zeng, 2024. "Tighter bound estimation for efficient biquadratic optimization over unit spheres," Journal of Global Optimization, Springer, vol. 90(2), pages 323-353, October.

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