A. V. Arutyunov, “Covering of nonlinear maps on a cone in neighborhoods of irregular points”, Mat. Zametki, 77:4 (2005), 483–497; Math. Notes, 77:4 (2005), 447

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Matematicheskie Zametki, 2005, Volume 77, Issue 4, Pages 483–497
DOI: https://doi.org/10.4213/mzm2507 (Mi mzm2507)

This article is cited in 20 scientific papers (total in 20 papers)

Covering of nonlinear maps on a cone in neighborhoods of irregular points

A. V. Arutyunov

Peoples Friendship University of Russia

Full-text PDF (258 kB) Citations (20)

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DOI: https://doi.org/10.4213/mzm2507

Abstract: Inverse function theorems for smooth nonlinear maps defined on convex cones in Banach spaces in a neighborhood of an irregular point are considered. The corresponding covering theorem is proved. The proofs are based on a Banach open mapping theorem for convex cones in Banach spaces, which is also proved in the paper. Sufficient conditions for tangency to the zero set of a nonlinear map without a priori regularity assumptions are obtained.

Received: 01.03.2004

English version:
Mathematical Notes, 2005, Volume 77, Issue 4, Pages 447–460
DOI: https://doi.org/10.1007/s11006-005-0043-x

Bibliographic databases:

UDC: 518.9

Language: Russian

Citation: A. V. Arutyunov, “Covering of nonlinear maps on a cone in neighborhoods of irregular points”, Mat. Zametki, 77:4 (2005), 483–497; Math. Notes, 77:4 (2005), 447–460

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https://doi.org/10.4213/mzm2507

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This publication is cited in the following 20 articles:

Andreas Fischer, Alexey F. Izmailov, Mario Jelitte, “Stability of Singular Solutions of Nonlinear Equations with Restricted Smoothness Assumptions”, J Optim Theory Appl, 196:3 (2023), 1008
Arutyunov A.V. Izmailov A.F., “Covering on a Convex Set in the Absence of Robinson'S Regularity”, SIAM J. Optim., 30:1 (2020), 604–629
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
Mordukhovich B., “Variational Analysis and Applications”, Variational Analysis and Applications, Springer Monographs in Mathematics, Springer International Publishing Ag, 2018, 1–622
Boris S. Mordukhovich, Springer Monographs in Mathematics, Variational Analysis and Applications, 2018, 103
Huynh Van Ngai, Thera M., “Directional Metric Regularity of Multifunctions”, Math. Oper. Res., 40:4 (2015), 969–991
A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russian Math. Surveys, 67:3 (2012), 403–457
Uderzo A., “On Mappings Covering at a Nonlinear Rate and their Perturbation Stability”, Nonlinear Anal.-Theory Methods Appl., 75:3 (2012), 1602–1616
Zhukovskii S.E., Mingaleeva Z.T., “Suschestvovanie i nepreryvnost neyavnoi funktsii v okrestnosti anormalnoi tochki”, Vestnik moskovskogo universiteta. seriya 15: vychislitelnaya matematika i kibernetika, 2 (2012), 10–15
S. E. Zhukovskii, Z. T. Mingaleeva, “Existence and continuity of an implicit function in the neighborhood of an abnormal point”, MoscowUniv.Comput.Math.Cybern., 36:2 (2012), 60
Arutyunov A.V., Zhukovskiy S.E., “Existence of local solutions in constrained dynamic systems”, Appl Anal, 90:6 (2011), 889–898
A. V. Arutyunov, “On implicit function theorems at abnormal points”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S18–S27
Arutyunov A. V., Avakov E. R., Izmailov A. F., “Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications”, Math. Program., 114:1, Ser. A (2008), 37–68
E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Necessary Conditions for an Extremum in a Mathematical Programming Problem”, Proc. Steklov Inst. Math., 256 (2007), 2–25
Arutyunov A. K., Izmailov A. F., “Directional stability theorem and directional metric regularity”, Math. Oper. Res., 31:3 (2006), 526–543
Avakov E. R., Arutyunov A. V., Izmailov A. F., “Necessary conditions for an extremum in 2-regular problems”, Dokl. Math., 73:3 (2006), 340–343
D. Yu. Karamzin, “On necessary extremum conditions for finite-dimensional problems with inequality constraints”, Comput. Math. Math. Phys., 46:11 (2006), 1860–1871
A. V. Arutyunov, “An implicit function theorem without a priori assumptions about normality”, Comput. Math. Math. Phys., 46:2 (2006), 195–205
A. V. Arutyunov, “Implicit-Function Theorem on the Cone in a Neighborhood of an Irregular Point”, Math. Notes, 78:4 (2005), 573–576
Arutyunov, AV, “Sensitivity analysis for cone-constrained optimization problems under the relaxed constraint qualifications”, Mathematics of Operations Research, 30:2 (2005), 333

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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