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On the strong metric subregularity in mathematical programming Cover

On the strong metric subregularity in mathematical programming

Open Access
|Jun 2022

References

  1. Bonnans, J.F. and Shapiro, A. (2000) Perturbation Analysis of Optimization Problems. Springer.10.1007/978-1-4612-1394-9
  2. Cibulka, R. Dontchev, A.L. and Kruger, A.Y. (2018) Strong metric subregularity of mappings in variational analysis and optimization. Journal of Mathematical Analysis and Application, 457: 1247–1282.10.1016/j.jmaa.2016.11.045
  3. Dmitruk, A.V. and Osmolovskii, N.P. (2018) A General Lagrange Multipliers Theorem and Related Questions. In: Control Systems and Mathematical Methods in Economics (Feichtinger et al., eds.), Lecture Notes in Economics and Mathematical Systems, 687: 165–194, Springer, Berlin.10.1007/978-3-319-75169-6_9
  4. Dontchev, A. L. and Rockafellar, R. T. (1998) Characterizations of Lipschitz stability in nonlinear programming. Mathematical Programming with Data Perturbations, 65–82, Lecture Notes in Pure and Appl. Math., 195, Dekker, New York.10.1201/9781003072119-4
  5. Dontchev, A. L. and Rockafellar, R. T. (2004) Regularity and conditioning of solution mappings in variational analysis. Set-Valued Analysis, 12: 79–109.10.1023/B:SVAN.0000023394.19482.30
  6. Dontchev, A. L. and Rockafellar, R. T. (2014) Implicit Functions and Solution Mappings: A View from Variational Analysis. Second edition. Springer, New York.10.1007/978-1-4939-1037-3
  7. Dubovitskii, A. Ya. and Milyutin, A.A. (1965) Extremum problems in the presence of restrictions. USSR Comput. Math. and Math. Phys., 5(3): 1–80,.10.1016/0041-5553(65)90148-5
  8. Hoffman, A.J. (1952) On approximate solutions of systems of linear inequalities. J. Res. Nat’l Bur. Standards 49: 263–265.10.6028/jres.049.027
  9. Ioffe, A.D. (1979) Regular points of Lipschitz functions. Trans. Am. Math. Soc. 251, 61–69.10.1090/S0002-9947-1979-0531969-6
  10. Ioffe, A.D. (2017) Variational Analysis and Regular Mappings. Springer.10.1007/978-3-319-64277-2
  11. Ioffe, A.D and Tikhomorov, V.M. (1974) Theory of Extremal Problems. Nauka, Moscow (in Russian); English translation: North Holland, 1979.
  12. Klatte, D. and Kummer, B. (2002) Nonsmooth Equations in Optimization. Kluwer Academic Publisher.
  13. Kyparisis, J. (1985) On uniqueness of Kuhn-Tucker multiplies in non-linear programming. Math. Programming, 32: 242–246.10.1007/BF01586095
  14. Levitin, E.S., Milyutin, A.A. and Osmolovskii, N.P. (1978) Higher-order local minimum conditions in problems with constraints. Uspekhi Mat. Nauk, 33: 8–148; English translation in Russian Math. Surveys, 33: 9–168.10.1070/RM1978v033n06ABEH003885
  15. Osmolovskii, N.P. and Veliov, V.M. (2021) On the strong subregularity of the optimality mapping in mathematical programming and calculus of variations. J. Math. Anal. Appl. 500(1), Article 125077.10.1016/j.jmaa.2021.125077
DOI: https://doi.org/10.2478/candc-2021-0027 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569
Language: English
Page range: 457 - 471
Submitted on: May 1, 2021
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Accepted on: Sep 1, 2021
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Published on: Jun 27, 2022
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2022 Nikolai P. Osmolovskii, Vladimir M. Veliov, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.