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

This article is cited in 13 scientific papers (total in 13 papers)

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

Full text: PDF file (214 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.9
Received: 13.10.1998
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
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    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  zmath  isi
    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  mathnet  mathscinet  zmath  elib
    3. Arutyunov, AV, “Abnormal equality-constrained optimization problems: sensitivity theory”, Mathematical Programming, 100:3 (2004), 485  crossref  mathscinet  zmath  isi  scopus  scopus
    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  mathnet  mathscinet  zmath
    5. A. V. Arutyunov, “Covering of nonlinear maps on a cone in neighborhoods of irregular points”, Math. Notes, 77:4 (2005), 447–460  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Arutyunov, AV, “Sensitivity analysis for cone-constrained optimization problems under the relaxed constraint qualifications”, Mathematics of Operations Research, 30:2 (2005), 333  crossref  mathscinet  zmath  isi  scopus  scopus
    7. A. F. Izmailov, “On the analytical and numerical stability of critical Lagrange multipliers”, Comput. Math. Math. Phys., 45:6 (2005), 930–946  mathnet  mathscinet  zmath  elib  elib
    8. A. V. Arutyunov, “An implicit function theorem without a priori assumptions about normality”, Comput. Math. Math. Phys., 46:2 (2006), 195–205  mathnet  crossref  mathscinet  zmath  elib  elib
    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  mathnet  crossref  mathscinet  zmath  elib  elib
    10. Brezhneva, OA, “Higher order implicit function theorems and degenerate nonlinear boundary-value problems”, Communications on Pure and Applied Analysis, 7:2 (2008), 293  crossref  mathscinet  zmath  isi
    11. A. V. Arutyunov, “On implicit function theorems at abnormal points”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S18–S27  mathnet  crossref  isi  elib
    12. E. R. Avakov, “Stability theorem and extremum conditions for abnormal problems”, Proc. Steklov Inst. Math., 291 (2015), 4–23  mathnet  crossref  crossref  isi  elib
    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  crossref  mathscinet  zmath  isi  scopus  scopus
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