Geodesic
Inhomogeneous convex approximations of nonsmooth functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 34-50

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In this paper we introduce notions of inhomogeneous upper convex and lower concave approximations of the increment of a nonsmooth function defined in a normed space and study exhaustive families of these approximations. In terms of the introduced notions we establish optimality conditions for various constrained and unconstrained extremum problems.
Keywords: nonsmooth analysis, inhomogeneous upper convex approximation, inhomogeneous lower concave approximation, exhaustive family of approximations, coexhauster. 
M. V. Dolgopolik. Inhomogeneous convex approximations of nonsmooth functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 34-50. http://geodesic.mathdoc.fr/item/IVM_2012_12_a3/
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