Error Bound for Generalized Linear Complementarity Problem Over an Affine Subspace and Its Applications

In this paper, we extended some results about the error bound estimation for linear complementarity problem to the generalized linear complementarity problem over an affine subspace (GLCP). More precisely, we first developed some new reformulations of the GLCP, and then we establish its global error bound estimation, based on which the famous Levenberg-Marquardt (L-M) algorithm is employed for obtaining its solution, and we show that the L-M algorithm is quadratically convergent without nondegenerate solution.