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Intersection Cuts for Nonlinear Integer Programming: Convexification Techniques for Structured Sets

Sina Modaresi (sim23***at***pitt.edu)
Mustafa Kilinc (mrk46***at***pitt.edu)
Juan Pablo Vielma (jvielma***at***mit.edu)

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.

Keywords: Split Cuts; Intersection Cuts; MINLP

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation:

Download: [PDF]

Entry Submitted: 02/11/2013
Entry Accepted: 02/11/2013
Entry Last Modified: 06/11/2014

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