title: The formula for the subdifferential of the distance function to a convex set in an nonsymmetrical space
metadata.name: dc.contributor.author
metadata.value: Abramova, Veronika V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Dudov, Sergei I.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zharkova, Anastasia V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-10-18T11:45:39Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-10-18T11:45:39Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Abramova V. V., Dudov S. I., Zharkova A. V. The formula for the subdifferential of the distance function to a convex set in an nonsymmetrical space. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 3, pp. 300–309.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16382
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The distance function, defined by the gauge (the Minkowsky gauge function) of a convex body compact, from a point to a convex closed set is considered in a finite-dimensional space. It is known that this function is convex in the whole space. The formula of its the subdifferential is obtained. It includes the subdifferential of gauge function and the cone of feasible directions of set to which the distance is measured, taken in one of the projection points on this set. This circumstans makes it different from the subdifferentional formula received earlier by B. N. Pshenichny in which another characteristics of the objects, defined the distance function, are used. Examples of applications of the obtained formula are given. In particular, a specific form of the subdifferential formula is given for the case when the set, the gauge of which specifies the distance function, and the set to which the distance is measured are lower Lebesgue sets of convex functions.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
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 15; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: distance function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: gauge of set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: subdifferential
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: support function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: cone of feasible directions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The formula for the subdifferential of the distance function to a convex set in an nonsymmetrical space
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 300-309.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16382/1/300-309.pdf
resources.format: Adobe PDF
resources.size: 281,04 kB