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

Guillaume Carlier (1) , Alfred Galichon (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 ECON - Département d'économie (Sciences Po)

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.

Domains: Humanities and Social Sciences; Economics and Finance

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⟩