Abstract

. 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 Luo and Tseng's, 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. Key words: Nonlinear complementarity problem, NCP-function, merit function, unconstrained optimization reformulation, error bound, bounded level sets. 3 The work of the second and third authors was supported in part by the Scienti c Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan. The work of the second author was also su...

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