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Contingent cone to a set defined by equality and inequality constraints at a Fréchet differentiable point. (English) Zbl 0803.49019

Summary: We prove equality expressions for the contingent cone and the strict normal cone to a set determined by equality and/or inequality constraints at a Fréchet differentiable point. A similar result has appeared before in the literature under the assumption that all the constraint functions of class \({\mathcal C}^ 1\) or under the assumption that the functions are strictly differentiable at the point in question. Our results has applications to the calculation of various kinds of tangent cones and normal cones.

MSC:

49J52 Nonsmooth analysis
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