“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

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Publisher
Springer Journals
Copyright
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

References

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