Calculus of Variations and Geometric Measure Theory

Behavior of the gradient flow: the convex case

Aris Daniilidis (Universitat Autònoma de Barcelona)

created by magnani on 16 Feb 2011

23 feb 2011


Dipartimento di Matematica - Sala Seminari - ore 18:00

ABSTRACT: The classical Lojasiewicz inequality and its extension to o-minimal structures by K. Kurdyka has a considerable impact on the analysis of gradient-like methods and related problems. In this talk we shall discuss alternative characterizations of this type of inequality via the notion of a defragmented gradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka-Lojasiewicz inequality is satisfied. Another characterization in terms of talweg lines will be given. In the convex case these results are significantly reinforced, allowing in particular to establish a kind of asymptotic equivalence for discrete gradient methods and continuous gradient curves. (Based on a joint work with J. Bolte, O. Ley and L. Mazet)