A polynomial-time algorithm to check closedness of simple second order mixed-integer sets

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Abstract

Let Lm be the Lorentz cone in ℝm. Given A ∈ ℚmxn1, and B ∈ ℚmxn2 and b ∈ ℚm, a simple second order conic mixed-integer set (SOCMIS) is a set of the form {(x, y) ∈ ℤn1 x ℝn2 | Ax + By - b ∈ Lm}. We show that there exists a polynomial-time algorithm to check the closedness of the convex hull of simple SOCMISs. Moreover, in the special case of pure integer problems, we present sufficient conditions, that can be checked in polynomial-time, to verify the closedness of intersection of simple SOCMISs.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 16th International Conference, IPCO 2013, Proceedings
Pages266-277
Number of pages12
DOIs
StatePublished - 2013
Externally publishedYes
Event16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013 - Valparaiso, Chile
Duration: 18 Mar 201320 Mar 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7801 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013
Country/TerritoryChile
CityValparaiso
Period18/03/1320/03/13

Keywords

  • Closedness
  • Mixed-integer convex programming
  • Polynomial-time algorithm

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