Statistical approximations for stochastic linear programming problems

Sampling and decomposition constitute two of the most successful approaches for addressing large-scale problems arising in statistics and optimization, respectively. In recent years, these two approaches have been combined for the solution of large-scale stochastic linear programming problems. This paper presents the algorithmic motivation for such methods, as well as a broad overview of issues in algorithm design. We discuss both basic schemes as well as computational enhancements and stopping rules. We also introduce a generalization of current algorithms to handle problems with random recourse.