1. Introduction
Society for Industrial and Applied Mathematics eBooks · 2009
1.1 Problem StatementThe linear complementarity problem consists in finding a vector in a finite-dimensional real vector space that satisfies a certain system of inequalities. Specifically, given a vector q∈Rn and a matrix M∈Rn×n , the linear complementarity problem, abbreviated LCP, is to find a vector z∈Rn such thatz≥0(1)q+Mz≥0(2)zT(q+Mz)=0(3)or to show that no such vector z exists. We denote the above LCP by the pair (q, M).Special instances of the linear complementarity problem can be found in the mathematical literature as early as 1940, but the problem received little attention until the mid 1960's at which time it became an object of study in its own right. Some of this early history is discussed in the Notes and References at the end of the chapter.