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

Author

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  • Guillaume Carlier

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Alfred Galichon

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Guillaume Carlier & Alfred Galichon, 2012. "Exponential convergence for a convexifying equation and a non-autonomous gradient ow for global minimization," Post-Print hal-01024585, HAL.
    • Handle: RePEc:hal:journl:hal-01024585
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01024585
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