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New bounds for nonconvex quadratically constrained quadratic programming

Zamani,Moslem
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.
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Publisher Copyright: © 2022, The Author(s).
Date
2023-03
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Tilburg University Research Output Collection
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Keywords
Quadratically constrained quadratic programming, Reformulation-linearization technique, Semidefinite relaxation
Citation
Zamani, M 2023, 'New bounds for nonconvex quadratically constrained quadratic programming', Journal of Global Optimization, vol. 85, pp. 595-613. https://doi.org/10.1007/s10898-022-01224-1
URI
https://hdl.handle.net/20.500.14602/78262
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