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Polyhedral Analysis and Branch-and-Cut for the Structural Analysis Problem

Lacroix, Mathieu; Mahjoub, Ali Ridha; Martin, Sébastien (2012), Polyhedral Analysis and Branch-and-Cut for the Structural Analysis Problem, in Paschos, Vangelis; Mahjoub, A. Ridha; Markakis, Vangelis; Milis, Ioannis, Combinatorial Optimization. Second International Symposium, ISCO 2012, Athens, Greece, April 19-21, 2012, Revised Selected Papers, Springer : Berlin Heidelberg, p. 117-128. 10.1007/978-3-642-32147-4_12

Type
Communication / Conférence
Date
2012
Conference title
Second International Symposium on Combinatorial Optimization, ISCO 2012
Conference date
2012-04
Conference city
Athènes
Conference country
Greece
Book title
Combinatorial Optimization. Second International Symposium, ISCO 2012, Athens, Greece, April 19-21, 2012, Revised Selected Papers; ISCO 2012
Book author
Paschos, Vangelis; Mahjoub, A. Ridha; Markakis, Vangelis; Milis, Ioannis
Publisher
Springer
Published in
Berlin Heidelberg
ISBN
978-3-642-32146-7
Pages
117-128
Publication identifier
Metadata
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Author(s)
Lacroix, Mathieu cc

Mahjoub, Ali Ridha
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Martin, Sébastien cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This consists, given a conditional differential-algebraic system, in verifying if the system is structurally solvable for every state, and if not in finding a state in which the system is structurally singular. In this paper we study this problem from a polyhedral point of view. We identify some classes of valid inequalities and characterize when these inequalities define facets for the associated polytope. Moreover, we devise separation routines for these inequalities. Based on this, we develop a Branch-and-Cut algorithm and present some experimental results.
Subjects / Keywords
Branch-and-Cut; Conditional Differential-algebraic system; bipartite graph; polytope; matching; structural analysis; facet