Concave Quadratic Cuts for Mixed-Integer Quadratic Problems

Jaehyun Park; Stephen Boyd

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arXiv · 1510.06421

Concave Quadratic Cuts for Mixed-Integer Quadratic Problems

Jaehyun Park·Stephen Boyd

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Abstract

The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold for any vector in the integer lattice ${\bf Z}^n$, and show that adding these inequalities to a mixed-integer nonconvex QCQP can improve the SDP-based bound on the optimal value. This scheme is tested using several numerical problem instances of the max-cut problem and the integer least squares problem.

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BibTeX RIS

Jaehyun Park, Stephen Boyd. 2016-09-28. Concave Quadratic Cuts for Mixed-Integer Quadratic Problems. https://arxiv.org/abs/1510.06421

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