Intersection cuts for nonlinear integer programming: convexification techniques for structured sets
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10107_2015_866_ReferencePDF.pdf
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Author(s)
Modaresi, Sina
Kılınç, Mustafa R.
Vielma Centeno, Juan Pablo
Date Issued
February 2015
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Modaresi, Sina, Mustafa R. Kılınç, and Juan Pablo Vielma. “Intersection Cuts for Nonlinear Integer Programming: Convexification Techniques for Structured Sets.” Math. Program. 155, no. 1–2 (February 17, 2015): 575–611.
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Author's final manuscript
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 conic 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.
MIT Department
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10107-015-0866-5
