Absil, Pierre-Antoine
[UCL]
Kurdyka, K
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. (c) 2006 Elsevier B.V. All rights reserved.
Bibliographic reference |
Absil, Pierre-Antoine ; Kurdyka, K. On the stable equilibrium points of gradient systems. In: Systems & Control Letters, Vol. 55, no. 7, p. 573-577 (2006) |
Permanent URL |
http://hdl.handle.net/2078.1/38453 |