REDUCING HORIZONTAL LINEAR COMPLEMENTARITY-PROBLEMS

In this note, we present an algorithm to reduce a horizontal linear co mplementarity problem (HLCP) to a standard linear complementarity prob lem (LCP) whenever it is possible to do so. In fact, the algorithm is just a specialization of the matroid intersection algorithm. We also s tudy the properties of matrix pairs that are analogous to the positive semidefiniteness and P- and P-o-properties of a square matrix, and sh ow that a large class of matrix pairs, including P-o-pairs, define red ucible HLCPs.