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Abstract and Applied Analysis
Volume 2013, Article ID 105930, 11 pages
Research Article

On Set-Valued Complementarity Problems

1Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, China
2Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan
3Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Received 18 September 2012; Accepted 14 December 2012

Academic Editor: Mohamed Tawhid

Copyright © 2013 Jinchuan Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper investigates the set-valued complementarity problems (SVCP) which poses rather different features from those that classical complementarity problems hold, due to tthe fact that he index set is not fixed, but dependent on . While comparing the set-valued complementarity problems with the classical complementarity problems, we analyze the solution set of SVCP. Moreover, properties of merit functions for SVCP are studied, such being as level bounded and error bounded. Finally, some possible research directions are discussed.