Second-order stochastic dominance constraints induced by mixed-integer linear recourse

We introduce stochastic integer programs with dominance constraints induced by mixed-integer lin-ear recourse. Closedness of the constraint set mapping with respect to perturbations of the underly-ing probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are identified. For these models, a decomposition algorithm is proposed. Computational tests with instances from power optimization and Sudoku puzzling conclude the paper. Key Words. Stochastic integer programming, stochastic dominance, mixed-integer optimization. AMS subject classifications. 90C15, 90C11, 60E15.