- Cutting-planes for optimization of convex functions over nonconvex sets Daniel Bienstock (danocolumbia.edu) Alexander Michalka (admichalkagmail.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: 05/19/2013Entry Accepted: 05/19/2013Entry Last Modified: 12/30/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.