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 x. 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.
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