Name
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. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.sysconle.2006.01.002 | Systems & Control Letters |
Keywords | Field | DocType |
Gradient flow,Lyapunov stability,Cost function,Local minimum | Lyapunov function,Mathematical optimization,Gradient descent,Control theory,Analytic function,Equilibrium point,Lyapunov stability,Maxima and minima,Smoothness,Balanced flow,Mathematics | Journal |
Volume | Issue | ISSN |
55 | 7 | 0167-6911 |
Citations | PageRank | References |
15 | 0.97 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| P.-A. Absil | 1 | 374 | 28.40 |
| Krzysztof Kurdyka | 2 | 20 | 3.60 |