The convex hull of a quadratic constraint over a polytope
Optimization and Control
2018-12-27 v1
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.
Keywords
Cite
@article{arxiv.1812.10160,
title = {The convex hull of a quadratic constraint over a polytope},
author = {Asteroide Santana and Santanu S. Dey},
journal= {arXiv preprint arXiv:1812.10160},
year = {2018}
}