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.
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Lacroix, M., Mahjoub, A.R., Martin, S. (2012). Polyhedral Analysis and Branch-and-Cut for the Structural Analysis Problem. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_12
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DOI: https://doi.org/10.1007/978-3-642-32147-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32146-7
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