Epiconvergence of relaxed stochastic optimization problem
Abstract
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.
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