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Cutting-planes for optimization of convex functions over nonconvex sets

Daniel Bienstock (dano***at***columbia.edu)
Alexander Michalka (admichalka***at***gmail.com)

Abstract: Motivated by mixed-integer, nonlinear optimization problems, we derive linear inequality characterizations for sets of the form conv{(x, q ) \in R^d × R : q \in Q(x), x \in R^d - int(P )} where Q is convex and differentiable and P \subset R^d . We show that in several cases our characterization leads to polynomial-time separation algorithms that operate in the original space of variables, in particular when Q is a positive-definite quadratic and P is a polyhedron or an ellipsoid.

Keywords: mixed-integer nonlinear programming, polynomial-time cutting-plane algorithms

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

Category 2: Convex and Nonsmooth Optimization

Category 3: Integer Programming (Cutting Plane Approaches )

Citation: May 2013

Download: [PDF]

Entry Submitted: 05/19/2013
Entry Accepted: 05/19/2013
Entry Last Modified: 12/30/2013

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