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2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.
In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary
optimality condition for an optimization problem which arise naturally from
a class of wide studied problems. In the second result we establish a sufficient
condition for the metric regularity of a set-valued map without continuity
assumptions.
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