Duality and approximation of stochastic optimal control problems under expectation constraints - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2021

Duality and approximation of stochastic optimal control problems under expectation constraints

Résumé

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is in duality with an optimization problem involving the Lagrange multiplier associated with the constraints. Then by convex analysis techniques, we provide a general existence result and some a priori estimation of the dual optimizers. We further provide a necessary and sufficient optimality condition for the initial constrained control problem. The same results are also obtained for a discrete time constrained control problem. Moreover, under additional regularity conditions, it is proved that the discrete time control problem converges to the continuous time problem, possibly with a convergence rate. This convergence result can be used to obtain numerical algorithms to approximate the continuous time control problem, which we illustrate by two simple numerical examples.
Fichier principal
Vignette du fichier
PTZ18_5.pdf (403.43 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02886824 , version 1 (01-07-2020)

Identifiants

Citer

Laurent Pfeiffer, Xiaolu Tan, Yulong Zhou. Duality and approximation of stochastic optimal control problems under expectation constraints. SIAM Journal on Control and Optimization, 2021, 59 (5), pp.3231-3260. ⟨10.1137/20M1349886⟩. ⟨hal-02886824⟩
42 Consultations
140 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More