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 Mat. Zametki, 2000, Volume 67, Issue 1, Pages 57–68 (Mi mz814)

Theorems on the representation of nonlinear mapping families and implicit function theorems

A. F. Izmailov

Dorodnitsyn Computing Centre of the Russian Academy of Sciences

DOI: https://doi.org/10.4213/mzm814

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English version:
Mathematical Notes, 2000, 67:1, 45–54

Bibliographic databases:

UDC: 517.9
Revised: 07.09.1999

Citation: A. F. Izmailov, “Theorems on the representation of nonlinear mapping families and implicit function theorems”, Mat. Zametki, 67:1 (2000), 57–68; Math. Notes, 67:1 (2000), 45–54

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Arutyunov, AV, “Inverse function theorem on a cone in the neighborhood of an abnormal point”, Doklady Mathematics, 67:2 (2003), 149
2. A. V. Arutyunov, A. F. Izmailov, “The sensitivity theory for abnormal optimization problems with equality constraints”, Comput. Math. Math. Phys., 43:2 (2003), 178–193
3. Arutyunov, AV, “Abnormal equality-constrained optimization problems: sensitivity theory”, Mathematical Programming, 100:3 (2004), 485
4. A. V. Arutyunov, A. F. Izmailov, “Sensitivity analysis for abnormal optimization problems with a cone constraint”, Comput. Math. Math. Phys., 44:4 (2004), 552–574
5. A. V. Arutyunov, “Covering of nonlinear maps on a cone in neighborhoods of irregular points”, Math. Notes, 77:4 (2005), 447–460
6. Arutyunov, AV, “Sensitivity analysis for cone-constrained optimization problems under the relaxed constraint qualifications”, Mathematics of Operations Research, 30:2 (2005), 333
7. A. F. Izmailov, “On the analytical and numerical stability of critical Lagrange multipliers”, Comput. Math. Math. Phys., 45:6 (2005), 930–946
8. A. V. Arutyunov, “An implicit function theorem without a priori assumptions about normality”, Comput. Math. Math. Phys., 46:2 (2006), 195–205
9. A. F. Izmailov, “Sensitivity of solutions to systems of optimality conditions under the violation of constraint qualifications”, Comput. Math. Math. Phys., 47:4 (2007), 533–554
10. Brezhneva, OA, “Higher order implicit function theorems and degenerate nonlinear boundary-value problems”, Communications on Pure and Applied Analysis, 7:2 (2008), 293
11. A. V. Arutyunov, “On implicit function theorems at abnormal points”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S18–S27
12. E. R. Avakov, “Stability theorem and extremum conditions for abnormal problems”, Proc. Steklov Inst. Math., 291 (2015), 4–23
13. Arutyunov A.V. Izmailov A.F., “Stability of Possibly Nonisolated Solutions of Constrained Equations, With Applications to Complementarity and Equilibrium Problems”, Set-Valued Var. Anal., 26:2 (2018), 327–352
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