English

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.

Keywords

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}
}
R2 v1 2026-06-22T07:23:22.376Z