Duality for mixed-integer convex minimization

Baes M, Oertel T, Weismantel R (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Mathematical Programming Springer Verlag (Germany)

Book Volume: 158

Pages Range: 547-564

Journal Issue: 1-2

DOI: 10.1007/s10107-015-0917-y

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

Authors with CRIS profile

Timm Oertel

Additional Organisation(s)

Professur für Mathematische Analyse von Daten (Data Analytics)

Involved external institutions

University of Zurich / Universität Zürich (UZH) CH Switzerland (CH) Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich CH Switzerland (CH)

How to cite

APA:

Baes, M., Oertel, T., & Weismantel, R. (2016). Duality for mixed-integer convex minimization. Mathematical Programming, 158(1-2), 547-564. https://dx.doi.org/10.1007/s10107-015-0917-y

MLA:

Baes, Michel, Timm Oertel, and Robert Weismantel. "Duality for mixed-integer convex minimization." Mathematical Programming 158.1-2 (2016): 547-564.

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