Epiconvergence of relaxed stochastic optimization problems
Published in Operations Research Letters, 2019
Recommended citation: Leclere, Vincent. "Epiconvergence of relaxed stochastic optimization problems." Operations Research Letters 47.6 (2019): 553-559. https://www.sciencedirect.com/science/article/pii/S0167637719302317
We consider relaxation of almost sure constraint in dynamic stochastic optimization problems and their convergence. We show an epiconvergence result relying on the Kudo convergence of -algebras and continuity of the objective and constraint operators. We present classical constraints and objective functions with conditions ensuring their continuity. We are motivated by a Lagrangian decomposition algorithm, known as Dual Approximate Dynamic Programming, that relies on relaxation, and can also be understood as a decision rule approach in the dual.