B. De Schutter and B. De Moor, "The extended linear complementarity problem and its applications in the max-plus algebra," in Complementarity and Variational Problems: State of the Art (M.C. Ferris and J.S. Pang, eds.), Philadelphia, Pennsylvania: SIAM, ISBN 0-89871-391-9, pp. 22-39, 1997.
In this paper we give a survey of our research on the Extended Linear Complementarity Problem (ELCP). First we discuss the link between the ELCP and other generalizations of the Linear Complementarity Problem, and we present an algorithm to find all the solutions of an ELCP. Next we introduce the max-plus algebra and show how it can be used to model a certain class of discrete event systems. Finally we show that the ELCP can be used to solve many important problems in the max-plus algebra.