DUALITY-BASED A POSTERIORI ERROR ESTIMATES FOR SOME APPROXIMATION SCHEMES FOR CONVEX OPTIMAL CONTROL PROBLEMS

Abstract : We introduce a class of numerical schemes for Hamilton-Jacobi-Bellman equations based on a novel Markov chain approximation of the associated optimal control problem, which uses, in turn, a piecewise constant policy approximation, Euler-Maruyama time stepping, and a Gauß-Hermite approximation of the Gaußian increments. We provide one-sided (lower) error bounds of order arbitrarily close to 1/2 in time and 1/3 in space for Lipschitz viscosity solutions, coupling probabilistic arguments with regularization techniques as introduced by Krylov. The order for sufficiently regular solutions is 1 in both time and space. For a class of convex problems arising in optimal investment, we use duality results to derive also a posteriori upper error bounds which are empirically of the same order as the lower bounds, as confirmed in our numerical tests.
Liste complète des métadonnées

Littérature citée [25 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01538617
Contributeur : Athena Picarelli <>
Soumis le : mardi 13 juin 2017 - 18:24:34
Dernière modification le : jeudi 29 juin 2017 - 01:04:26

Fichier

Error_Posteriori.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01538617, version 1

Collections

Citation

Athena Picarelli, Christoph Reisinger. DUALITY-BASED A POSTERIORI ERROR ESTIMATES FOR SOME APPROXIMATION SCHEMES FOR CONVEX OPTIMAL CONTROL PROBLEMS. 2017. 〈hal-01538617〉

Partager

Métriques

Consultations de
la notice

43

Téléchargements du document

33