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B. C Eaves, H. Scarf, The solution of systems of piecewise linear equations, Math. Oper. Res., 1 (1976) 1-27.

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Article

General Characterization of a Linear Complementarity Problem

1Analysis, Modeling and Simulation Laboratory, University Hassan II Casablanca, Morocco

2MPD Laboratory, UCAM, Marrakech, Morocco and UMI UMMISCO, IRD - UPMC, Paris, France


American Journal of Modeling and Optimization. 2013, Vol. 1 No. 1, 1-5
DOI: 10.12691/ajmo-1-1-1
Copyright © 2013 Science and Education Publishing

Cite this paper:
Youssef Elfoutayeni, Mohamed Khaladi. General Characterization of a Linear Complementarity Problem. American Journal of Modeling and Optimization. 2013; 1(1):1-5. doi: 10.12691/ajmo-1-1-1.

Correspondence to: Youssef Elfoutayeni, Analysis, Modeling and Simulation Laboratory, University Hassan II Casablanca, Morocco. Email: youssef_foutayeni@yahoo.fr

Abstract

For a given matrix and a vector of, the linear complementarity problem LCP(A,b) is to find a vector in satisfying, and or showing that such a vector does not exist. Under various hypotheses on the matrix, LCP (A,b) was studied by many authors in the last decade. In previous papers we have developed algorithms for solving some classes of LCP (A,b). In this work, we give a general characterization of the solutions of LCP (A,b), we show under what conditions the problem has a solution or not and how to calculate the solution when they exist. We then apply this characterization to some examples and find the solutions or show that the problem LCP (A,b) has no solution.

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