On the equivalence of linear complementarity problems

B. Schutter, de; W.P.M.H. Heemels; A. Bemporad

doi:10.1016/S0167-6377(02)00159-1

On the equivalence of linear complementarity problems

B. Schutter, de, W.P.M.H. Heemels, A. Bemporad

Research output: Contribution to journal › Article › Academic › peer-review

23 Citations (Scopus)

Abstract

We show that the Extended Linear ComplementarityProblem (ELCP) can be recast as a standard Linear ComplementarityProblem(LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since manyextensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP aswell. 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.

Original language	English
Pages (from-to)	211-222
Journal	Operations Research Letters
Volume	30
Issue number	4
DOIs	https://doi.org/10.1016/S0167-6377(02)00159-1
Publication status	Published - 2002

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title = "On the equivalence of linear complementarity problems",

abstract = "We show that the Extended Linear ComplementarityProblem (ELCP) can be recast as a standard Linear ComplementarityProblem(LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since manyextensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP aswell. 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.",

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AU - Schutter, de, B.

AU - Heemels, W.P.M.H.

AU - Bemporad, A.

PY - 2002

Y1 - 2002

N2 - We show that the Extended Linear ComplementarityProblem (ELCP) can be recast as a standard Linear ComplementarityProblem(LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since manyextensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP aswell. 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.

AB - We show that the Extended Linear ComplementarityProblem (ELCP) can be recast as a standard Linear ComplementarityProblem(LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since manyextensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP aswell. 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.

U2 - 10.1016/S0167-6377(02)00159-1

DO - 10.1016/S0167-6377(02)00159-1

M3 - Article

SN - 0167-6377

VL - 30

SP - 211

EP - 222

JO - Operations Research Letters

JF - Operations Research Letters

IS - 4

ER -

On the equivalence of linear complementarity problems

Abstract

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