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Decomposition of convex high dimensional aggregative stochastic control problems

Seguret, Adrien; Alasseur, Clémence; Bonnans, Joseph Frédéric; de Paola, Antonio; Oudjane, Nadia; Trovato, Vincenzo (2023), Decomposition of convex high dimensional aggregative stochastic control problems, Applied Mathematics and Optimization, 88, 8, p. 35. 10.1007/s00245-023-09977-1

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Type
Article accepté pour publication ou publié
Date
2023
Journal name
Applied Mathematics and Optimization
Volume
88
Number
8
Publisher
Springer
Published in
Paris
Pages
35
Publication identifier
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Author(s)
Seguret, Adrien
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie [EDF R&D OSIRIS]
Alasseur, Clémence
Laboratoire de Finance des Marchés d'Energie [FiME Lab]
Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie [EDF R&D OSIRIS]
Bonnans, Joseph Frédéric
Laboratoire des signaux et systèmes [L2S]
de Paola, Antonio
Department of Electrical and Electronic Engineering [London] [DEEE]
Oudjane, Nadia
Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie [EDF R&D OSIRIS]
Trovato, Vincenzo
Department of Electrical and Electronic Engineering [London] [DEEE]
Department of civil, environmental and mechanical engineering [Trento]
Abstract (EN)
We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some reasonable assumptions an ε-optimal solution of the original problem. As second contribution, we present a decentralized algorithm whose convergence to the solution of the modified problem is established. Finally, we study the application of the developed tools in an engineering context, studying a coordination problem for large populations of domestic thermostatically controlled loads.
Subjects / Keywords
Stochastic optimization; Lagrangian decomposition; Uzawa's algorithm; Stochastic gradient