Duality for mixed-integer convex minimization

• 成果类型: Article
• 署名作者: Baes, Michel; Oertel, Timm; Weismantel, Robert
• 署名单位: University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0917-y
• 发表日期: 2016
• 页码: 547-564
• 关键词: relaxations; hierarchy

摘要

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 mixed-integer-free polyhedra. Our optimality conditions allow us to define an exact dual of our original mixed-integer convex problem.