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Centerpoints: a link between optimization and convex geometry

Amitabh, Basu and Oertel, Timm 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 Springer, pp. 14-25. 10.1007/978-3-319-33461-5 2

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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: Mathematics
Publisher: Springer
ISBN: 9783319334608
ISSN: 0302-9743
Date of First Compliant Deposit: 30 June 2016
Date of Acceptance: 31 March 2016
Last Modified: 25 Jan 2018 15:35
URI: http://orca.cf.ac.uk/id/eprint/92247

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