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Semidefinite Programming Based Convex Relaxation for Nonconvex Quadratically Constrained Quadratic Programming

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications (WCGO 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 991))

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Abstract

In this paper, we review recent development in semidefinite programming (SDP) based convex relaxations for nonconvex quadratically constrained quadratic programming (QCQP) problems. QCQP problems have been well known as NP-hard nonconvex problems. We focus on convex relaxations of QCQP, which forms the base of global algorithms for solving QCQP. We review SDP relaxations, reformulation-linearization technique, SOC-RLT constraints and various other techniques based on lifting and linearization.

Supported by Shanghai Sailing Program 18YF1401700, Natural Science Foundation of China (NSFC) 11801087 and Hong Kong Research Grants Council under Grants 14213716 and 14202017.

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Jiang, R., Li, D. (2020). Semidefinite Programming Based Convex Relaxation for Nonconvex Quadratically Constrained Quadratic Programming. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_22

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