phone +7 (3412) 91 60 92
mail imi@udsu.ru
ru-RU Russian
Home » Issues » Archive of Issues » 2022 - 3 issue » pp. 403-414

Archive of Issues

Turkey Eskişehir; Sivas
Year
2022
Volume
32
Issue
3
Pages
403-414
<<
>>
Section Mathematics
Title Upper and lower directional derivative sets and differentials of the set valued maps
Author(-s) Ege N.a, Huseyin A.b, Huseyin N.b
Affiliations Eskişehir Technical Universitya, Sivas Cumhuriyet Universityb
Abstract In this paper directional derivative sets and differentials of a given set valued map are studied. Different type relations between directional derivative sets and differentials of a set valued map are specified. It is established that every compact subset of lower derivative set can be used for lower approximation of given set valued map. Upper and lower contingent cones of some plane sets are calculated and compared.
Keywords set valued map, contingent cone, differential, directional derivative set, Hausdorff deviation
UDC 517.977
MSC 26E25, 54C60
DOI 10.35634/vm220304
Received 2 August 2022
Language English
Citation Ege N., Huseyin A., Huseyin N. Upper and lower directional derivative sets and differentials of the set valued maps, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 3, pp. 403-414.
References
  1. Aubin J.-P., Frankowska H. Set-valued analysis, Boston: Birkhäuser, 1990.
  2. Deimling K. Multivalued differential equations, Berlin: De Gruyter, 1992. https://doi.org/10.1515/9783110874228
  3. Krasovskii N.N., Subbotin A.I. Game-theoretical control problems, New York: Springer, 1988.
  4. Panasenko E.A., Rodina L.I., Tonkov E.L. Asymptotically stable statistically weakly invariant sets for controlled systems, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, vol. 16, no. 5, pp. 135-142 (in Russian). http://mi.mathnet.ru/eng/timm615
  5. Subbotin A.I. Generalized solutions of first-order PDEs. The dynamical optimization perspective, Boston: Birkhäuser, 1995.
  6. Tolstonogov A.A. Differential inclusions in a Banach space with composite right-hand side, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, vol. 26, no. 1, pp. 212-222. https://doi.org/10.21538/0134-4889-2020-26-1-212-222
  7. Clarke F.H. Optimization and nonsmooth analysis, New York: John Wiley and Sons, 1983.
  8. Dem'yanov V.F., Rubinov A.M. Osnovy negladkogo analiza i kvazidifferentsial'noe ischislenie (Foundations of nonsmooth analysis and quasidifferential calculus), Moscow: Nauka, 1990.
  9. Mordukhovich B.S. Variational analysis and generalized differentiation. II. Applications, Berlin: Springer, 2006. https://doi.org/10.1007/3-540-31246-3
  10. Ushakov V.N., Guseinov Kh.G., Latushkin Ya.A., Lebedev P.D. On the coincidence of maximal stable bridges in two approach game problems for stationary control systems, Proceedings of the Steklov Institute of Mathematics, 2010, vol. 268, suppl. 1, pp. 240-263. https://doi.org/10.1134/S0081543810050172
  11. Ushakov V.N., Zimovets A.A. Invariance defect of sets with respect to differential inclusion, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2011, issue 2, pp. 98-111 (in Russian). https://doi.org/10.20537/vm110207
  12. Aubin J.-P. Contingent derivatives of set valued maps and existence of solutions to nonlinear inclusions and differential inclusions, New York: Acad. Press, 1981, pp. 159-229.
  13. Guseinov Kh.G., Subbotin A.I., Ushakov V.N. Derivatives for multivalued mappings with applications to game-theoretical problems of control, Problems of Control and Information Theory, 1985, vol. 14, no. 3, pp. 155-167.
  14. Hukuhara H. Intégration des applications mesurables dont la valeur est un compact convexe, Funkcialaj Ekvacioj, 1967, vol. 10, no. 3, pp. 205-223 (in French).
  15. Michel P., Penot J.-P. Subdifferential calculus for Lipschitzian and non-Lipschitzian functions, Comptes Rendus de l'Académie des Sciences - Séries I, 1984, vol. 298, no. 12, pp. 269-272.
  16. Polovinkin E.S. Mnogoznachnyi analiz i differentsial'nye vklyucheniya (Set-valued analysis and differential inclusions), Moscow: Fizmatlit, 2015.
  17. Ursesku C. Tangent sets' calculus and necessary conditions for extremality, SIAM Journal on Control and Optimization, 1982, vol. 20, issue 4, pp. 563-574. https://doi.org/10.1137/0320041
  18. Polovinkin E.S. Teoriya mnogoznachnykh otobrazhenii (Theory of set-valued maps), Moscow: Moscow Institute of Physics and Technology, 1983.
  19. Bouligand G. Sur l'existence des demi-tangents à une courbe de Jordan, Fundamenta Mathematicae, 1930, vol. 15, no. 1, pp. 215-218. https://doi.org/10.4064/fm-15-1-215-218
Full text
/doc/issues-2022/22-03-04.pdf
<< Previous article
Next article >>