Max-plus-algebraic Problems and the Extended Linear Complementarity Problem - Algorithmic Aspects

Many fundamental problems in the max-plus-algebraic system theory for discrete event systems — among which the minimal state space realization problem — can be solved using an Extended Linear Complementarity Problem (ELCP). We present some new, more efficient methods to solve the ELCP. We show that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (LCP). Our proof results in three possible numerical solution methods for a given ELCP: regular ELCP algorithms, mixed integer linear programming algorithms, and regular LCP algorithms. We also apply these three methods to a basic max-plus-algebraic benchmark problem.