Duality for Mixed-Integer Convex Minimization
Optimization and Control
2014-12-09 v1
Abstract
We extend in two ways the standard Karush-Kuhn-Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard Karush-Kuhn-Tucker conditions involve separating hyperplanes, our extension is based on lattice-free polyhedra. Our optimality conditions allow us to define an exact dual of our original mixed-integer convex problem.
Cite
@article{arxiv.1412.2515,
title = {Duality for Mixed-Integer Convex Minimization},
author = {Michel Baes and Timm Oertel and Robert Weismantel},
journal= {arXiv preprint arXiv:1412.2515},
year = {2014}
}