Centerpoints: a link between optimization and convex geometry

Amitabh, Basu and Oertel, Timm ORCID: https://orcid.org/0000-0001-5720-8978 2016. Centerpoints: a link between optimization and convex geometry. Presented at: IPCO 2016: International Conference on Integer Programming and Combinatorial Optimization, Liege, Belgium, 1-3 June 2016. Published in: Louveaux, Quentin and Skutella, Martin eds. Integer Programming and Combinatorial Optimization: 18th International Conference, IPCO 2016, Liège, Belgium, June 1-3, 2016, Proceedings. Lecture Notes in Computer Science: Integer Programming and Combinatorial Optimization. Lecture Notes in Computer Science , vol.9682 Springer, pp. 14-25. 10.1007/978-3-319-33461-5

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Abstract

We introduce a concept that generalizes several different notions of a “centerpoint” in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based on centerpoints are “best possible” in a certain sense. Motivated by this, we establish several structural results about this concept and provide efficient algorithms for computing these points.

Item Type:	Conference or Workshop Item (Paper)
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Springer
ISBN:	9783319334608
ISSN:	0302-9743
Date of First Compliant Deposit:	30 June 2016
Date of Acceptance:	31 March 2016
Last Modified:	26 Nov 2024 01:45
URI:	https://orca.cardiff.ac.uk/id/eprint/92247

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