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Acta Mathematica Vietnamica

ON THE ROCKAFELLAR DERIVATIVE OF MARGINAL FUNCTIONS AND APPLICATIONS

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Abstract

In this paper, some evaluations of the directional Rockafellar derivative of a function defined by φF(x)=inf{f(x,y)|yF(x)} via the directional Clarke and Rockafellar derivative of f are shown. These evaluations are applied to find necessary optimality conditions for generalized optimal control problems governed by hemivariational inequalities.