Combinatorial optimization model and MIP formulation for the structural analysis of conditional differential-algebraic systems

Authors:
Mathieu Lacroix;A. Ridha Mahjoub;Sébastien Martin
Affiliations:
LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France and LIMOS, Université Blaise Pascal Clermont-Ferrand II, Complexe Scientifi ...;LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France;LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France
Venue:
Computers and Industrial Engineering
Year:
2011

Citing 4
Cited 2

Computing the structural index

SIAM Journal on Algebraic and Discrete Methods
An O(EV log V) algorithm for finding a maximal weighted matching in general graphs

SIAM Journal on Computing
The consistent intialization of differential-algebraic systems

SIAM Journal on Scientific and Statistical Computing
Matrices and Matroids for Systems Analysis

Matrices and Matroids for Systems Analysis

On the NP-completeness of the perfect matching free subgraph problem

Theoretical Computer Science
Polyhedral analysis and branch-and-cut for the structural analysis problem

ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This problem consists, given a conditional differential-algebraic system, in verifying if the system is structurally nonsingular for every state, and if not in finding a state in which the system is structurally singular. We give a formulation for this problem as an integer linear program. This is based on a transformation of the problem into a matching problem in an auxiliary graph. We also show that the linear relaxation of that formulation can be solved in polynomial time. Using this, we develop a Branch-and-Cut algorithm for solving the problem and present some experimental results.