Polyhedral analysis and branch-and-cut for the structural analysis problem

Authors:
Mathieu Lacroix;A. Ridha Mahjoub;Sébastien Martin
Affiliations:
LIPN CNRS UMR 7030, Université Paris 13, Villetaneuse, France;LAMSADE, CNRS UMR 7243, Université Paris-Dauphine, Paris Cedex 16, France;LAMSADE, CNRS UMR 7243, Université Paris-Dauphine, Paris Cedex 16, France
Venue:
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Year:
2012

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Abstract

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.