Epiconvergence of relaxed stochastic optimization problem

Vincent Leclère (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

In this paper we consider the relaxation of a dynamic stochastic optimization problem where we replace a stochastic constraint - for example an almost sure constraint - by a conditional expectation constraint. We show an epiconvergence result relying on the Kudo convergence of $\sigma-$algebra and continuity of the objective and constraint operators. We also present some classicals constraints in stochastic optimization and give some conditions insuring their continuity. We conclude with a decomposition algorithm that uses such a relaxation.

Mots clés: Epiconvergence; Stochastic Optimization; Constraints Aggregation; Conditional expectation; Constraints Approximation

Domaines: Optimisation et contrôle [math.OC]

Vincent Leclère. Epiconvergence of relaxed stochastic optimization problem. 2013. ⟨hal-00848275v1⟩