Duality for mixed-integer convex minimization

Baes, Michel, Oertel, Timm ORCID: https://orcid.org/0000-0001-5720-8978 and Weismantel, Robert 2016. Duality for mixed-integer convex minimization. Mathematical Programming 158 , pp. 547-564. 10.1007/s10107-015-0917-y

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer Verlag
ISSN:	0025-5610
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	15 May 2015
Last Modified:	29 Nov 2024 12:15
URI:	https://orca.cardiff.ac.uk/id/eprint/86769

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