Intersection cuts for nonlinear integer programming: convexification techniques for structured sets
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 geom...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/103100 https://orcid.org/0000-0003-4335-7248 |
| Summary: | 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. |
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