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New bounds for nonconvex quadratically constrained quadratic programming

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  • Moslem Zamani

    (Tilburg University)

Abstract

In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs (QCQPs). We propose two types of bounds for QCQPs, quadratic and cubic bounds. We use affine functions as Lagrange multipliers for quadratic bounds. We demonstrate that most semidefinite relaxations can be obtained as the dual of a quadratic bound. In addition, we study bounds obtained by changing the ground set. For cubic bounds, in addition to affine multipliers we employ quadratic functions. We provide a comparison between the proposed cubic bound and typical bounds for standard quadratic programs. Moreover, we report comparison results of some quadratic and cubic bounds.

Suggested Citation

  • Moslem Zamani, 2023. "New bounds for nonconvex quadratically constrained quadratic programming," Journal of Global Optimization, Springer, vol. 85(3), pages 595-613, March.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:3:d:10.1007_s10898-022-01224-1
    DOI: 10.1007/s10898-022-01224-1
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    References listed on IDEAS

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    1. Moslem Zamani, 2019. "A new algorithm for concave quadratic programming," Journal of Global Optimization, Springer, vol. 75(3), pages 655-681, November.
    2. A. Sutou & Y. Dai, 2002. "Global Optimization Approach to Unequal Global Optimization Approach to Unequal Sphere Packing Problems in 3D," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 671-694, September.
    3. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, December.
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