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A characterization of paratingent cone and \(P\)-subderivative with applications in nonsmooth analysis. (English) Zbl 0744.49006
Characterizations of the paratingent cone to an open set at a boundary point and the \(P\)-directional derivative of a real-valued continuous function are given by using the contingent cone and the contingent directional derivative, respectively. It is shown that these results are useful to establish sufficient condition for strict differentiability of a continuous function. The \(P\)-subderivative is also introduced and its applications to a continuous mathematical programming problem subject to a set constraint is reported.
MSC:
49J52 Nonsmooth analysis
90C48 Programming in abstract spaces
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