New NCP-functions and their properties

Recently, Luo and Tseng proposed a class of merit functions for the nonlinear complementarity problem (NCP) and showed that it enjoys several interesting properties under some assumptions. In this paper, adopting a similar idea to that of Luo and Tseng, we present new merit functions for the NCP, which can be decomposed into component functions. We show that these merit functions not only share many properties with the one proposed by Luo and Tseng but also enjoy additional favorable properties owing to their decomposable structure. In particular, we present fairly mild conditions under which these merit functions have bounded level sets.