**Reference:**

B. De Schutter,
W.P.M.H. Heemels, and
A. Bemporad,
"Max-plus-algebraic problems and the extended linear complementarity
problem - Algorithmic aspects," *Proceedings of the 15th IFAC World
Congress (b'02)*, Barcelona, Spain, pp. 151-156, July 2002.

**Abstract:**

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.

Online version of the paper

Corresponding technical report: pdf file (118 KB)

@inproceedings{DeSHee:01-15,

author={B. {D}e Schutter and W.P.M.H. Heemels and A. Bemporad},

title={Max-plus-algebraic problems and the extended linear complementarity problem -- {Algorithmic} aspects},

booktitle={Proceedings of the 15th IFAC World Congress (b'02)},

address={Barcelona, Spain},

pages={151--156},

month=jul,

year={2002},

doi={10.3182/20020721-6-ES-1901.00513}

}

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