Displaying similar documents to “Exponential convergence for a convexifying equation”

Exponential convergence for a convexifying equation

Guillaume Carlier, Alfred Galichon (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an evolution equation similar to that introduced by Vese in [ (1999) 1573–1591] 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.

Exponential convergence for a convexifying equation

Guillaume Carlier, Alfred Galichon (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider an evolution equation similar to that introduced by Vese in [24 (1999) 1573–1591] 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.

Lipschitz modulus in convex semi-infinite optimization d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem's data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably...

Weighted energy-dissipation functionals for gradient flows

Alexander Mielke, Ulisse Stefanelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate a global-in-time variational approach to abstract evolution by means of the functionals proposed by Mielke and Ortiz [ (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization. Applications...

Weighted energy-dissipation functionals for gradient flows

Alexander Mielke, Ulisse Stefanelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We investigate a global-in-time variational approach to abstract evolution by means of the functionals proposed by Mielke and Ortiz [ (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization. Applications...