Some new existence, sensitivity and stability results for the nonlinear complementarity problem

Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Concepción, Chile; rlopez@ucsc.cl

Received: 12 July 2006
Revised: 15 January 2007

Abstract

In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence results, which extend and generalize most of the existing ones from the literature. Such results are given in terms of some sets called coercive existence sets, which we also employ for obtaining new sensitivity and stability results. Topological properties of the solution-set-mapping and bounds for it are also established. Finally, we deal with the piecewise affine case.