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Implicit function theorem as a realization of the Lagrange principle. Abnormal points

descriptionPublicationkeyboard_double_arrow_right Article 28 Feb 2000 Russian Federation Publisher:Steklov Mathematical InstituteJournal:Sbornik: Mathematics, volume 191, pages 1-24 (issn: 1064-5616, eissn: 1468-4802, Copyright policy )
Authors: Arutyunov A.V.;

doi: 10.1070/sm2000v191n01abeh000446

Implicit function theorem as a realization of the Lagrange principle. Abnormal points

Abstract

The author proves a generalization of the implicit function theorem to the case in which the normality condition fails (the relevant reference point is then called abnormal). The analysis rests on second-order optimality conditions in constrained optimization. The results of the article were announced in Dokl. Akad. Nauk Ross. Akad. Nauk 368, 586-589 (1999) (Russian).

Country
Russian Federation
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Keywords

330, implicit function theorem, Abstract inverse mapping and implicit function theorems involving nonlinear operators, abnormal point, derivation, second-order condition, 510

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Average
Top 10%
Average
Green