Applications of Degree Theory to Linear Complementarity Problems
M. Seetharama Gowda · Mathematics of Operations Research · 1993
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 P 0 -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.