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arXiv · 2610.16116

On the convexification of a bilinearly constrained set with a common variable

Hyun-Ju Oh·Boshi Yang
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Abstract

We study the convexification of sets defined by box constraints and bilinear inequality constraints in which all bilinear terms share a common variable. For this structured class of nonconvex sets, we provide a complete characterization of the extreme points of the convex hull and derive an explicit description of all facet-defining inequalities, thereby obtaining a full polyhedral description of the convex hull. In addition, we develop a polynomial-time separation algorithm for the facet-defining inequalities and illustrate its effectiveness through examples. These results offer both structural insight into the geometry of the convex hull and algorithmic tools for identifying violated inequalities.

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Hyun-Ju Oh, Boshi Yang. 2026-10-12. On the convexification of a bilinearly constrained set with a common variable. https://arxiv.org/abs/2610.16116

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