Article Dans Une Revue Journal of Optimization Theory and Applications Année : 2026

Differentiability and Regularization of Parametric Convex Value Functions in Stochastic Multistage Optimization

Résumé

In multistage decision problems, it is often the case that an initial strategic decision (such as investment) is followed by many operational ones (operating the investment). Such initial strategic decision can be seen as a parameter affecting a multistage decision problem. More generally, we study in this paper a standard multistage stochastic optimization problem depending on a parameter. When the parameter is fixed, Stochastic Dynamic Programming provides a way to compute the optimal value of the problem. Thus, the value function depends both on the state (as usual) and on the parameter. Our aim is to investigate on the possibility to efficiently compute gradients of the value function with respect to the parameter, when these objects exist. When nondifferentiable, we propose a regularization method based on the Moreau-Yosida envelope. We present a numerical test case from day-ahead power scheduling.

Fichier principal
Vignette du fichier
preprint_v2_parametric.pdf (774.18 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-03903218 , version 1 (16-12-2022)
hal-03903218 , version 2 (11-01-2023)
hal-03903218 , version 3 (16-03-2026)

Licence

Identifiants

Citer

Adrien Le Franc, Pierre Carpentier, Jean-Philippe Chancelier, Michel de Lara. Differentiability and Regularization of Parametric Convex Value Functions in Stochastic Multistage Optimization. Journal of Optimization Theory and Applications, 2026, 208 (3), pp.111. ⟨10.1007/s10957-025-02876-1⟩. ⟨hal-03903218v2⟩
691 Consultations
812 Téléchargements

Altmetric

Partager

  • More