Paper ID sheet - Systems and Control Engineering at ULg
- TITLE: On the stable equilibrium points of gradient systems
- AUTHORS: 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.
- STATUS: Systems & Control Letters, Volume 55, Issue 7, July 2006, Pages 573-577.
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",