• TITLE: On the stable equilibrium points of gradient systems
• AUTHORS: P.-A. Absil, K. Kurdyka.
• ABSTRACT:
  This paper studies the relations between the local minima of a cost function $f$ and the stable equilibria of the gradient descent flow of $f$. In particular, it is shown that, under the assumption that $f$ is real analytic, local minimality is necessary and sufficient for stability. Under the weaker assumption that $f$ is indefinitely continuously differentiable, local minimality is neither necessary nor sufficient for stability.
• STATUS: Systems & Control Letters, Volume 55, Issue 7, July 2006, Pages 573-577.

• Published version: http://dx.doi.org/10.1016/j.sysconle.2006.01.002.
• Preprint [pdf].
• Related paper: Convergence of the Iterates of Descent Methods for Analytic Cost Functions.

Bibtex citation:

@ARTICLE{AbsKur2006,
  author = "Absil, P.-A. and Kurdyka, K.",
  title = "On the stable equilibrium points of gradient systems",
  journal = "Systems Control Lett.",
  fjournal = "Systems \& Control Letters",
  year = 2006,
  month = "July",
  volume = 55,
  number = 7,
  pages = "573--577",
  doi = "10.1016/j.sysconle.2006.01.002",
}