Classes of functions and feasibility conditions in nonlinear complementarity problems

Abstract

Given a mappingF from real Euclideann-space into itself, we investigate the connection between various known classes of functions and the nonlinear complementarity problem: Find anx* such thatFx* ? 0 andx* ? 0 are orthogonal. In particular, we study the extent to which the existence of au ? 0 withFu ? 0 (feasible point) implies the existence of a solution to the nonlinear complementarity problem, and extend, to nonlinear mappings, known results in the linear complementarity problem on P-matrices, diagonally dominant matrices with non-negative diagonal elements, matrices with off-diagonal non-positive entries, and positive semidefinite matrices.