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arXiv · 2208.00345

Solving sparse separable bilinear programs using lifted bilinear cover inequalities

Xiaoyi Gu·Santanu S. Dey·Jean-Philippe P. Richard
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Abstract

Recently, we proposed a class of inequalities called lifted bilinear cover inequalities, which are second-order cone representable convex inequalities, and are valid for a set described by a separable bilinear constraint together with bounds on variables. In this paper, we study the computational potential of these inequalities for separable bilinear optimization problems. We first prove that the semi-definite programming relaxation provides no benefit over the McCormick relaxation for such problems. We then design a simple randomized separation heuristic for lifted bilinear cover inequalities. In our computational experiments, we separate many rounds of these inequalities starting from McCormick's relaxation of instances where each constraint is a separable bilinear constraint set. We demonstrate that there is a significant improvement in the performance of a state-of-the-art global solver in terms of gap closed, when these inequalities are added at the root node compared to when they are not.

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Xiaoyi Gu, Santanu S. Dey, Jean-Philippe P. Richard. 2022-07-31. Solving sparse separable bilinear programs using lifted bilinear cover inequalities. https://arxiv.org/abs/2208.00345

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