On the equivalence of linear complementarity problems

Authors:
B. De Schutter;W. P. M. H. Heemels;A. Bemporad
Affiliations:
Control Systems Engineering, Fac. ITS, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands;Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Dip. Ingegneria dell'Informazione, Universití di Siena, Via Roma 56, 53100 Siena, Italy
Venue:
Operations Research Letters
Year:
2002

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Abstract

We show that the Extended Linear Complementarity Problem (ELCP) can be recast as a standard Linear Complementarity Problem (LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since many extensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP as well. Our equivalence proof is constructive and leads to three possible numerical solution methods for a given ELCP: regular ELCP algorithms, mixed integer linear programming algorithms, and regular LCP algorithms.