English

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}
}