descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book , Preprint , Conference object 01 Jan 2016Embargo end date: 01 Jan 2015 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Optimization, volume 27, pages 866-889 (issn: 1052-6234, eissn: 1095-7189,

Authors: Basu, Amitabh; Oertel, Timm;

doi: 10.1137/16m1092908 , 10.1007/978-3-319-33461-5_2 , 10.48550/arxiv.1511.08609

arXiv: 1511.08609

Centerpoints: A Link between Optimization and Convex Geometry

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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. Our main motivation is to understand the complexity of oracle based convex mixed-integer optimization.

Related Organizations

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Keywords

Convex programming, Helly-type theorems and geometric transversal theory, Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry), convex mixed-integer optimization, convex and discrete geometry, Mixed integer programming, Optimization and Control (math.OC), FOS: Mathematics, centerpoints, 52A35, 52C07, 90C11, 90C25, QA, Mathematics - Optimization and Control

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