Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2022, Volume 18, Issue 4, Pages 535–547
DOI: https://doi.org/10.21638/11701/spbu10.2022.408
(Mi vspui554)
 

Applied mathematics

Smooth approximations of nonsmooth convex functions

L. N. Polyakova

St Petersburg State University, 7–9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
References:
Abstract: 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, infimal convolution operation, smooth approximation.
Received: July 21, 2022
Accepted: September 1, 2022
Document Type: Article
Language: English
Citation: L. N. Polyakova, “Smooth approximations of nonsmooth convex functions”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 18:4 (2022), 535–547
Citation in format AMSBIB
\Bibitem{Pol22}
\by L.~N.~Polyakova
\paper Smooth approximations of nonsmooth convex functions
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2022
\vol 18
\issue 4
\pages 535--547
\mathnet{http://mi.mathnet.ru/vspui554}
\crossref{https://doi.org/10.21638/11701/spbu10.2022.408}
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    Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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