Algorithms for the Linear Complementarity Problem Which Allow an Arbitrary Starting Point

Abstract

The linear complementarity problem with data q ɛ Rⁿ and M ɛ R^n×n consists in finding two vectory s and z in Rⁿ such that(1.1)

$${\text{s = Mz + q ,}}$$

(1.1)

(1.2)

$$s,\;z\; \ge \;0\;,$$

(1.2)

(1.3)

$${s_i}{z_{i\;}} = \;0\;,\;i\; = \;1,\;2, \ldots ,\;n\;.$$

(1.3)

.

The research in this paper was supported by the Office of Naval Research Contract Number N00014-77C-0518. We also are grateful to the referees for their helpful comments.