Abstract : We consider an evolution equation similar to that introduced by Vese in [10] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time. We then introduce a non-autonomous gradient flow and prove that its trajectories all converge to minimizers of the convex envelope.
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Soumis le : mercredi 16 juillet 2014 - 13:08:02
Dernière modification le : lundi 17 juin 2019 - 18:26:08
Document(s) archivé(s) le : lundi 24 novembre 2014 - 16:18:04
Guillaume Carlier, Alfred Galichon. Exponential convergence for a convexifying equation and a non-autonomous gradient ow for global minimization. Control, Optimisation and Calculus of Variations, 2012, 18 (3), pp.611-620. ⟨hal-01024585⟩
