title: Reduction and minimality of coexhausters
metadata.name: dc.contributor.author
metadata.value: Abbasov, Majid E.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-26T09:14:17Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-26T09:14:17Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Abbasov M. E. Reduction and minimality of coexhausters. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 1, pp. 3–13.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.101
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9493
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: V. F. Demyanov introduced exhausters for the study of nonsmooth functions. These are
  families of convex compact sets that allow to represent the main part of the increment of a
  considered function in a neighborhood of a studied point in a form of MaxMin or MinMax of
  linear functions. Optimality conditions were described in terms of these objects. This paved
  a way for construction of new algorithms for solving nondifferentiable optimization problems.
  Exhausters are not uniquely defined. It is obvious that the smaller the exhauster is the lesser
  computational expenses are when working with it. Thus, problem of reduction of an available
  family arises. This problem was first considered by V. A. Roshchina. She proposed conditions
  for minimality and described some methods for the reduction in case when these conditions
  were not satisfied. However, it turned out that the exhauster mapping is not continuous in
  the Hausdorff metrics, what leads to the problems with convergence of numerical methods.
  To overcome this difficulty V. F. Demyanov proposed coexhausters notion. These objects
  allow to represent the main part of the increment of considered functions in a neighborhood
  of a studied point in the form of MaxMin or MinMax of affine functions. One can determine
  a class of functions with continuous coexhauster mapping. Optimality conditions can be
  described in terms of these objects, too. But coexhausters are also not uniquely defined. The
  problem of coexhausters reduction is considered in this paper for the first time. Definitions
  of minimality proposed by V. A. Roshchina are used. In contrast to ideas proposed in the
  works of V. A. Roshchina, conditions of minimality and the technique of reduction developed
  in this paper have a clear and transparent geometric interpretation.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант №16-31-00056 мол_а).
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. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: coexhausters
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: nonsmooth analysis
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: nondifferentiable optimization
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Reduction and minimality of coexhausters
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Abbasov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9493/1/01-Abbasov.pdf
resources.format: Adobe PDF
resources.size: 422,43 kB