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Optimality conditions in variational form for non-linear constrained stochastic control problems

Laurent Pfeiffer 1
1 COMMANDS - Controle, Optimisation, modèles, Méthodes et Applications pour les Systèmes Dynamiques non linéaires
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the probability distribution of the state variable at the final time. The analysis uses in an essential manner a convexity property of the set of reachable probability distributions. An augmented Lagrangian method based on the obtained optimality conditions is proposed and analyzed for solving iteratively the problem. At each iteration of the method, a standard stochastic optimal control problem is solved by dynamic programming. Two academical examples are investigated.
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https://hal.inria.fr/hal-03113195
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Submitted on : Monday, January 18, 2021 - 11:47:26 AM
Last modification on : Saturday, May 1, 2021 - 3:39:22 AM
Long-term archiving on: : Monday, April 19, 2021 - 6:40:10 PM

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Laurent Pfeiffer. Optimality conditions in variational form for non-linear constrained stochastic control problems. Mathematical Control & Related Fields, 2020, 10 (3), pp.493-526. ⟨10.3934/mcrf.2020008⟩. ⟨hal-03113195⟩

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