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arXiv · 1812.10160

The convex hull of a quadratic constraint over a polytope

Asteroide Santana·Santanu S. Dey
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Abstract

A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving non-convex QCQP to global optimality is a well-known NP-hard problem and a traditional approach is to use convex relaxations and branch-and-bound algorithms. This paper makes a contribution in this direction by showing that the exact convex hull of a general quadratic equation intersected with any bounded polyhedron is second-order cone representable. We present a simple constructive proof of this result.

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Asteroide Santana, Santanu S. Dey. 2018-12-25. The convex hull of a quadratic constraint over a polytope. https://arxiv.org/abs/1812.10160

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