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, 2018, Volume 14, Issue 1, Pages 20–30
DOI: https://doi.org/10.21638/11701/spbu10.2018.103 (Mi vspui354) 		 
Applied mathematics

The quasidifferential calculus, separation of convex sets and the Demyanov difference

J. Grzybowskia, D. Pallaschkeb, R. Urbańskia

a Adam Mickiewicz University, 87, ul. Umultowska, Pozna, ZIP: 61-614, Poland
b Karlsruhe Institute of Technology University, 89, Kaiserstrasse, Karlsruhe, ZIP: 76-133, Germany
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DOI: https://doi.org/10.21638/11701/spbu10.2018.103
Abstract: In this paper we give a survey of the influence of the quasidifferential calculus of V. F. Demyanov and A. M. Rubinov to the field of generalized convexity. In particular, we will show the strong relations between the order cancellation property of bounded closed convex set and the separation property of bounded closed convex sets by sets. Moreover, a generalization of the Demyanov difference of compact convex sets infinite dimension and its role in the context of convex sets by sets is discussed. Refs 15. Figs 2.
Keywords: quasidifferential calculus, convex sets, subdifferential calculus, generaliz convexity.
Received: October 15, 2017
Accepted: January 11, 2018
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: English
Citation: J. Grzybowski, D. Pallaschke, R. Urbański, “The quasidifferential calculus, separation of convex sets and the Demyanov difference”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 14:1 (2018), 20–30
Citation in format AMSBIB
\Bibitem{GrzPalUrb18}
\by J.~Grzybowski, D.~Pallaschke, R.~Urba\'nski
\paper The quasidifferential calculus, separation of convex sets and the Demyanov difference
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2018
\vol 14
\issue 1
\pages 20--30
\mathnet{http://mi.mathnet.ru/vspui354}
\crossref{https://doi.org/10.21638/11701/spbu10.2018.103}
\elib{https://elibrary.ru/item.asp?id=32786041}
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    		Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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    References:15
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