Journal of Convex Analysis 24 (2017), No. 1, 287--303
Copyright Heldermann Verlag 2017
Calculation of Subdifferentials for the Difference of Two Convex Functions
Evgeny Sergeevich Polovinkin
Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny -- Moscow region, Russia 141700
polovinkin@mail.mipt.ru
It is shown that for some classes of functions all epiderivatives and subdifferentials of F.H.Clarke type and P.Michel--J.-P.Penot type and others coincide. Several rules of calculation of subdifferentials for the difference of two convex functions are obtained. Some examples are considered.
Keywords: Set-valued map, tangent cone, convex function, semiregular function, Lipschitz continuity, epiderivatives, subdifferentials.
MSC: 49K22, 49K24; 49J22, 49J24
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