Reducing horizontal linear complementarity problems

In this note, we present an algorithm to reduce a horizontal linear complementarity problem (HLCP) to a standard linear complementarity problem (LCP) whenever it is possible to do so. In fact, the algorithm is just a specialization of the matroid intersection algorithm. We also study the properties of matrix pairs that are analogous to the positive semidefiniteness and P- and P0-properties of a square matrix, and show that a large class of matrix pairs, including P0-pairs, define reducible HLCPs.