Existence theory for the complex nonlinear complementarity problem

Abstract

The main result in this paper is an existence theorem for the following complex nonlinear complementarity problem: find z such thatwhere S is a polyhedral cone in Cn, S* the polar cone, and g is a mapping from Cn into itself. It is shown that the above problem has a unique solution if the mapping g is continuous and strongly monotone on the polyhedral cone S.