Paper ID sheet UCL-INMA-2005.137


On the stable equilibrium points of gradient systems

P.-A. Absil, K. Kurdyka
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.
Key words
BibTeX entry

  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",
Further information
Related paper: Convergence of the Iterates of Descent Methods for Analytic Cost Functions