“Facet” separation with one linear program

“Facet” separation with one linear program Math. Program., Ser. A https://doi.org/10.1007/s10107-018-1299-8 FULL LENGTH PAPER 1 2 Michele Conforti · Laurence A. Wolsey Received: 12 August 2016 / Accepted: 16 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018 Abstract Given polyhedron P and and a point x , the separation problem for polyhe- dra asks to certify that x ∈ P and if not, to determine an inequality that is satisﬁed by P and violated by x . This problem is repeatedly solved in cutting plane methods for Integer Programming and the quality of the violated inequality is an essential feature in the performance of such methods. In this paper we address the problem of ﬁnding efﬁciently an inequality that is violated by x and either deﬁnes an improper face or a facet of P. We show that, by solving a single linear program, one almost surely obtains such an improper face or facet. Keywords Integer programming · Separation problem · Polyhedra · Extended formulations · Facets · Cutting plane algorithm · Split inequalities Mathematics Subject Classiﬁcation 90C27 · 90C57 1 Introduction Given a polyhedron P and a point x ,the separation problem asks to either certify that ∗ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Programming Springer Journals

“Facet” separation with one linear program

Mathematical Programming, Volume OnlineFirst – May 28, 2018
20 pages

/lp/springer_journal/facet-separation-with-one-linear-program-PcPJGQBl0t
Publisher
Springer Journals
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0025-5610
eISSN
1436-4646
D.O.I.
10.1007/s10107-018-1299-8
Publisher site
See Article on Publisher Site

Abstract

Math. Program., Ser. A https://doi.org/10.1007/s10107-018-1299-8 FULL LENGTH PAPER 1 2 Michele Conforti · Laurence A. Wolsey Received: 12 August 2016 / Accepted: 16 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018 Abstract Given polyhedron P and and a point x , the separation problem for polyhe- dra asks to certify that x ∈ P and if not, to determine an inequality that is satisﬁed by P and violated by x . This problem is repeatedly solved in cutting plane methods for Integer Programming and the quality of the violated inequality is an essential feature in the performance of such methods. In this paper we address the problem of ﬁnding efﬁciently an inequality that is violated by x and either deﬁnes an improper face or a facet of P. We show that, by solving a single linear program, one almost surely obtains such an improper face or facet. Keywords Integer programming · Separation problem · Polyhedra · Extended formulations · Facets · Cutting plane algorithm · Split inequalities Mathematics Subject Classiﬁcation 90C27 · 90C57 1 Introduction Given a polyhedron P and a point x ,the separation problem asks to either certify that ∗

Journal

Mathematical ProgrammingSpringer Journals

Published: May 28, 2018

DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create folders to

Export folders, citations