GENERALIZATIONS OF P-0-PROPERTIES AND P-PROPERTIES - EXTENDED VERTICAL AND HORIZONTAL LINEAR COMPLEMENTARITY-PROBLEMS

Generalizing the concept of W-o-pair of Willson, we introduce the noti ons of column (row) W-o- and column (row) W-properties for a set of k + 1 square matrices (M(o), M1,..., M(k)) (Df the same dimension), wher e k greater than or equal to 1. When k = 1 and M(o), = I, these reduce to the familiar P-o- and P-properties of a square matrix. We show tha t these notions are related to the extended vertical and horizontal LC Ps. Specifically, we show that these notions appear in certain feasibl e/infeasible interior point algorithms and that the column (row) W-pro perty is characterized by the unique solvability in extended horizonta l (vertical) LCPs. As a by-product of our analysis, we show that a mon otone horizontal LCP is equivalent to a (standard) LCP and that for a monotone horizontal LCP, feasibility implies solvability.