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. 
@article{IVM_2012_12_a3,
     author = {M. V. Dolgopolik},
     title = {Inhomogeneous convex approximations of nonsmooth functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {34--50},
     publisher = {mathdoc},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_12_a3/}
}
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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/