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2012 | 66 | 2 |
Tytuł artykułu

Generalization of p-regularity notion and tangent cone description in the singular case

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
Rocznik
Tom
66
Numer
2
Opis fizyczny
Daty
wydano
2012
online
2016-07-25
Bibliografia
  • Brezhneva, O. A., Tret’yakov, A. A., New Methods for Solving Singular Nonlinear Problems, Moscow, 2000 (Russian).
  • Brezhneva, O. A., Tret’yakov, A. A., Optimality conditions for degenerate extremum problems with equality contractions, SIAM J. Control Optim. 42, no. 2 (2003), 725-745.
  • Ioffe, A. D., Tihomirov, V. M., Theory of Extremal Problems, North-Holland, Studies in Mathematics and its Applications, Amsterdam, 1979.
  • Izmailov, A. F., Tret‘yakov, A. A., Factor-analysis of Nonlinear Mappings, Nauka, Moscow, 1994 (Russian).
  • Izmailov, A. F., Tret’yakov, A. A., 2-regular solutions of nonlinear problems, Theory and numerical methods, Fizmatlit., Nauka, Moscow, 1999 (Russian).
  • Musielak, A., Linear Operators, PWN, Warszawa, 1987 (Polish).
  • Niczyporowicz, E., The Flat Curves. Selected Problems in Analytic and Differential Geometry, PWN, Warszawa, 1991 (Polish).
  • Prusińska, A., Trety’akov, A., A remark on existence of solutions to nonlinear equations with degenerate mappings, Set-Valued Var. Anal. 16 (2008), 93-104.
  • Tret’yakov, A. A., Marsden, J. E., Factor-analysis of nonlinear mappings: p-regularity theory, Commun. Pure Appl. Anal. 2, no. 4 (2003), 425-445.
  • Tret’yakov, A. A., Necessary and Sufficient Conditions for Optimality of p-th Order, Control and Optimization, Moscow, MSU, 1983, 28-35 (Russian).
  • Tret’yakov, A. A., Necessary and sufficient conditions for optimality of p-th order, Zh. Vychisl. Mat. i Mat. Fiz. 24 (1984), 123-127 (Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2012_66_2_63-79
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