title: Smooth approximations of nonsmooth convex functions
metadata.name: dc.contributor.author
metadata.value: Polyakova, Lyudmila N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-14T14:44:12Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-14T14:44:12Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Polyakova, L. N. (2023). Smooth approximations of nonsmooth convex functions. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 18(4), 535-547.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.408
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39311
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 18; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: set-valued mapping
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: semicontinuous mapping
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: conjugate function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Kuratowski converge
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: infimal convolution operation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: smooth approximation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Smooth approximations of nonsmooth convex functions
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15529-Текст статьи-52261-1-10-20230308.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39311/1/15529-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-52261-1-10-20230308.pdf
resources.format: Adobe PDF
resources.size: 568,32 kB