On the equivalence of linear complementarity problems

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