Intersection cuts for nonlinear integer programming: convexification techniques for structured sets
Author(s)Modaresi, Sina; Kılınç, Mustafa R.; Vielma Centeno, Juan Pablo
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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.
DepartmentSloan School of Management
Springer Berlin Heidelberg
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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