document: Sufficient conditions on nonemptiness and boundedness of the solution set of the P/sub 0 / function nonlinear complementarity problem The P/sub 0 / function nonlinear complementarity , problem -LRB- NCP -RRB- 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/sub 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/sub 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/sub 0 / function NCP is bounded
doc_bio_tags: B I O B O B O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O
extractive_keyphrases: sufficient conditions nonemptiness boundedness solution set
abstractive_keyphrases: p/sub 0/ function nonlinear complementarity problem