Sufficient conditions on nonemptiness and boundedness of the solution set of the P0 function nonlinear complementarity problem

Authors:
Zhenghai Huang
Affiliations:
Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2734, Beijing 100080, China
Venue:
Operations Research Letters
Year:
2002

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Abstract

Recently, the P"0 function nonlinear complementarity problem (NCP) has attracted a lot of attention among researchers. Various assumed conditions, which ensure that the NCP has a solution have been proposed. In this paper, by using the notion of an exceptional family of elements we develop a sufficient condition which ensures that the solution set of the P"0 function NCP is nonempty and bounded. In particular, we prove that many existing assumed conditions imply this sufficient condition. Thus, these conditions imply that the solution set of the P"0 function NCP is nonempty and bounded. In addition, we also prove directly that a few existence conditions imply that the solution set of the P"0 function NCP is bounded.