Applications of Degree Theory to Linear Complementarity Problems

In this paper, we consider two applications of degree theory to linear complementarity problems. In the first application, we study the stability of an LCP at a solution point. Specifically we prove the stability of an LCP corresponding to a P₀-matrix at an isolated solution. Using a recent degree formula due to Stewart 1991, we strengthen a stability result of Gowda and Pang 1992. In the second application, we use the same degree formula of Stewart to describe the number of solutions of LCP(M, q) when M is a negative almost N-matrix. This analysis leads to a Lipschitzian characterization of the solution map Φ: q ↦ SOL(M, q) corresponding to a nondegenerate negative matrix.