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Structural Analysis for Differential-Algebraic Systems : Complexity, formulation and facets

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Date
2010
Dewey
Recherche opérationnelle
Sujet
structural analysis; Differential algebraic system; facet; polytope; matching; bipartite graph
Journal issue
Electronic Notes in Discrete Mathematics
Volume
36
Publication date
2010
Article pages
1073-1080
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.endm.2010.05.136
Conference name
ISCO International Symposium on Combinatorial Optimization
Conference date
03-2010
Conference city
Hammamet
Conference country
Tunisie
URI
https://basepub.dauphine.fr/handle/123456789/4027
Collections
  • LAMSADE : Publications
Metadata
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Author
Mahjoub, Ali Ridha
Lacroix, Mathieu
Martin, Sébastien
Type
Communication / Conférence
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 wellconstrained for every state and if not in finding a state for which the system is bad-constrained. We first show that the problem reduces to the perfect matching free subgraph problem in a bipartite graph. We then show the NP-completeness of this problem and give a formulation as an integer linear program.We also discuss the polytope of the solutions of this problem and propose a Branch-and-Cut algorithm.

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