On the stable equilibrium points of gradient systems

Absil, Pierre-Antoine;Kurdyka, K
(2006) Systems & Control Letters — Vol. 55, n° 7, p. 573-577 (2006)

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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.
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Absil, P.-A., & Kurdyka, K. (2006). On the stable equilibrium points of gradient systems. Systems & Control Letters, 55(7), 573-577. https://doi.org/10.1016/j.sysconle.2006.01.002 (Original work published 2006)