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Journal Articles Control, Optimisation and Calculus of Variations Year : 2012

Exponential convergence for a convexifying equation and a non-autonomous gradient ow for global minimization

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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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Dates and versions

hal-01024585 , version 1 (16-07-2014)

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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⟩
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