Functions Without Exceptional Family of Elements and Complementarity Problems1

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Abstract

In Ref. 1, Isac, Bulavski, and Kalashnikov introduced the concept of exceptional family of elements for a continuous function f: Rn→Rn. It is known that, if there does not exist an exceptional family of elements for f, then the corresponding complementarity problem has a solution. In this paper, we show that several classes of nonlinear functions, known in complementarity theory or other domains, are functions without exceptional family of elements and consequently the corresponding complementarity problem is solvable. It is evident that the notion of exceptional family of elements provides an alternative way of determining whether or not the complementarity problem has a solution.

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