Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Matematicheskie Zametki, 2025, Volume 118, Issue 6, Pages 824–843
DOI: https://doi.org/10.4213/mzm14705 (Mi mzm14705) 		 
On the stability of saddle points

A. V. Arutyunov, S. E. Zhukovskiy

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
Full-text PDF (597 kB) First page English version article
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm14705
Abstract: The stability of saddle points is studied. A stability theorem is proved and examples showing that its assumptions are essential are presented. Generalizations of the stability theorem are obtained. The notion of a generalized saddle point is discussed, and properties and stability of such points are studied.
Keywords: saddle point, generalized saddle point, stability.
Received: 10.04.2025
Revised: 23.06.2025
Accepted: 20.07.2025
Published: 15.12.2025
English version:
Mathematical Notes, 2025, Volume 118, Issue 6, Pages 1178–1192
DOI: https://doi.org/10.1134/S0001434625605660
Document Type: Article
UDC: 517
MSC: 90C31
Language: Russian
Citation: A. V. Arutyunov, S. E. Zhukovskiy, “On the stability of saddle points”, Mat. Zametki, 118:6 (2025), 824–843; Math. Notes, 118:6 (2025), 1178–1192
Citation in format AMSBIB
\Bibitem{AruZhu25}
\by A.~V.~Arutyunov, S.~E.~Zhukovskiy
\paper On the stability of saddle points
\jour Mat. Zametki
\yr 2025
\vol 118
\issue 6
\pages 824--843
\mathnet{http://mi.mathnet.ru/mzm14705}
\crossref{https://doi.org/10.4213/mzm14705}
\transl
\jour Math. Notes
\yr 2025
\vol 118
\issue 6
\pages 1178--1192
\crossref{https://doi.org/10.1134/S0001434625605660}
Linking options:
  • https://www.mathnet.ru/eng/mzm14705
  • https://doi.org/10.4213/mzm14705
  • https://www.mathnet.ru/eng/mzm/v118/i6/p824
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2026