Geodesic
Smooth approximations of nonsmooth convex functions
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 4, pp. 535-547

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For an arbitrary convex function, using the infimal convolution operation, a family of continuously differentiable convex functions approximating it is constructed. The constructed approximating family of smooth convex functions Kuratowski converges to the function under consideration. If the domain of the considered function is compact, then such smooth convex approximations are uniform in the Chebyshev metric. The approximation of a convex set by a family of smooth convex sets is also considered.
Keywords: set-valued mapping, semicontinuous mapping, conjugate function, Kuratowski converge, smooth approximation.
Mots-clés : infimal convolution operation 
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     author = {L. N. Polyakova},
     title = {Smooth approximations of nonsmooth convex functions},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {535--547},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2022_18_4_a7/}
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L. N. Polyakova. Smooth approximations of nonsmooth convex functions. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 4, pp. 535-547. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_4_a7/