Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Polovinkin E. S. On Relationship between Derivative of Multifunction and Its Support Function. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 1, pp. 13-21. DOI: 10.18500/1816-9791-2013-13-1-1-13-21, EDN: SMXXFN

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.02.2013
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.9
DOI: 
10.18500/1816-9791-2013-13-1-1-13-21
EDN: 
SMXXFN

On Relationship between Derivative of Multifunction and Its Support Function

Autors: 
Polovinkin Evgeny Sergeevich, Moscow Institute of Physics and Technology (State University)
Abstract: 

We obtain sufficient conditions under which the support function of the derivative of a set-valued mapping coincides with the derivative of the support function of a set-valued mapping in some sence. The example showing the difference between these concepts and the example of a Lipschitz set-valued mapping whose support function at any point does not have the mixed derivatives are obtained.

Key words: 
tangent cones
derivative of multifunctions
support function
References: 
  1. Aubin J.-P. Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions and differential inclusions // Advances in Math. Suppl. Studies. 1981. Vol. 7A. P. 160–272.
  2. Половинкин Е. С. Теория многозначных отображений. М. : Изд-во МФТИ, 1983. 108 c. [Polovinkin E. S. The theory of multi-valued mappings. Moscow : Moscow Institute of Physics and Technology, 1983. 108 p.]
  3. Половинкин Е. С., Балашов М. В. Элементы выпуклого и сильно выпуклого анализа. М. : Физматлит, 2007. 440 c. [Polovinkin E. S., Balashov M. V. Elements of convex and strongly convex analysis. Moscow: Fizmatlit, 2007. 440 p.]
  4. Рокафеллар Р. Выпуклый анализ. М. : Мир, 1973. 472 c. [Rockafellar R. T. Convex analysis. Princeton, New Jersey : Princeton university press, 1970. 472 p.]
  5. Пшеничный Б. Н. Выпуклый анализ и экстремальные задачи. М. : Наука, 1980. 320 c. [Pshenichny B. N. Convex analysis and extremal problems. Moscow : Nauka, 1980. 320 p.]
  6. Aubin J.-P., Frankovska H. Set-Valued Analisys. Boston; Basel; Berlin : Birkhӓuser, 1990. 464 p.
  7. Aubin J.-P. Lipschitz behavior of solutions to convex minimization problems // Math. of Oper. Res. 1984. Vol. 9. P. 87–111.
  8. Колмогоров А. Н., Фомин С. В. Элементы теории функций и функционального анализа. М. : Наука, 1975. 496 c. [Kolmogorov A. N., Fomin S. V. Elements of the theory of functions and functional analysis. Moscow : Nauka, 1975. 496 p.]
Received: 
25.08.2012
Accepted: 
16.01.2013
Published: 
15.02.2013
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