Regularity, calmness and support principle

The paper deals with necessary optimality conditions for a mathematical programming problem whose constraints are given by set-valued maps in Banach spaces. The normality of the problem is assured by a regularity condition which is a generalization of that introduced by Zowe-Kurcyusz-Penot in the case of single-valued maps. It is shown that the regularity condition implies also the calmness in the sense of Clarke for the problem under consideration. A new concept of prederivative of set-valued maps is used as the main tool for provide the results of the paper.

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