A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse (Q623459)

Inclusion of stochastic dominance constraints into stochastic programming models enables to incorporate random benchmarks instead of fixed thresholds. This paper elaborates on second-order dominance constraints in the framework of recourse models with mixed-integer linear recourse. First, closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. This key result opens the possibility to rely on approximation schemes based on discretization of probability measures and to solve the related large-scale, block-structured, mixed-integer linear programs. For these models, a decomposition algorithm is proposed and tested on problems from power optimization. The large-scale experiments indicate the superiority of the decomposition approach to an application of \texttt{Cplex}.