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April 3, 2026Mathematical Notes2 citations

On the Stability of Saddle Points

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AAA. V. ArutyunovSZS. E. Zhukovskii

Key Points

  • The aim is to investigate the stability of saddle points and prove a relevant stability theorem.
  • Studied saddle points and formulated a stability theorem.
  • Presented examples to demonstrate necessity of assumptions in the theorem.
  • Discussed generalizations of the stability theorem and properties of generalized saddle points.
  • Proved a theorem regarding the stability of saddle points.
  • Provided critical examples highlighting the assumptions needed for stability.
  • Explored new generalizations of the original stability theorem.

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.

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Cite This Study

Arutyunov et al. (2025) studied this question.

synapsesocial.com/papers/69cf5dc55a333a821460bc70https://doi.org/10.1134/s0001434625605660
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