Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 94, Issue 2, Pages 183-199Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
DOI: 10.1016/j.matpur.2010.03.007
Keywords
Planar dynamical system; Gradient trajectory; Convex function; Convex foliation; Lojasiewicz inequality
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Funding
- MEC (Spain) [MTM2008-06695-C03-03]
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We hereby introduce and study the notion of self-contracted curves, which encompasses orbits of gradient systems of convex and quasiconvex functions. Our main result shows that bounded self-contracted planar curves have a finite length. We also give an example of a convex function defined in the plane whose gradient orbits spiral infinitely many times around the unique minimizer of the function. (C) 2010 Elsevier Masson SAS. All rights reserved.
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