Essential intersection and approximation results for robust optimization (Q2925036)

The authors develop a finite approximation of a robust stochastic program, understood as an optimization problem with a set of random constraints that have to be satisfied almost surely. The finite approximation is built via selecting finitely many constraints using an ergodic measure-preserving transformation on the underlying probability space. As a consequence of Poincaré's recurrence theorem, the procedure selects a scenario in each predefined positive probability set in finitely many steps. Results of ergodic theory allow to prove a convergence of the sequence of optimal solutions to the true solution under several mild assumptions provided that the constraints are convex or at least inf-compact on some positive probability set. The contribution is mainly theoretical and connects elements of ergodic theory and optimization in an elegant way. No numerical applications are mentioned.