On degeneracy in linear complementarity problems (Q5916363)

Let \(M\) be an \(n\times n\) matrix and \(q\) an \(n\)-dimensional vector. The linear complementarity problem is to determine \(x\geq 0\) such that \(w=Mx+q\geq 0\) and \(x^ Tw=0\). A solution \(x\) for which \(x_ i=w_ i=0\) for at least one \(i\) is termed degenerate. \textit{K. G. Murty} [Linear Algebra Appl. 5, 65-108 (1972; Zbl 0241.90046)] has defined the notion of parity of a set of nondegenerate solutions. In this paper the notion of parity is extended to a set which may contain both degenerate and nondegenerate solutions and properties of this notion are studied.