Intersection Cuts for Nonlinear Integer Programming: Convexification Techniques for Structured Sets
Abstract
We study the generalization of split, k-branch split, and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference between a convex set and an open set with a simple geometric structure. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split, k-branch split, and intersection cuts for several classes of non-polyhedral sets. In particular, we give simple formulas for split cuts for essentially all convex sets described by a single quadratic inequality. We also give simple formulas for k-branch split cuts and some general intersection cuts for a wide variety of convex quadratic sets.
Cite
@article{arxiv.1302.2556,
title = {Intersection Cuts for Nonlinear Integer Programming: Convexification Techniques for Structured Sets},
author = {Sina Modaresi and Mustafa R. Kılınç and Juan Pablo Vielma},
journal= {arXiv preprint arXiv:1302.2556},
year = {2014}
}