Sample approximation technique for mixed-integer stochastic programming problems with expected value constraints

Abstract

This paper deals with the theory of sample approximation techniques applied to stochastic programming problems with expected value constraints. We extend the results of Branda (Optimization 61(8):949–968, 2012c) and Wang and Ahmed (Oper Res Lett 36:515–519, 2008) on the rates of convergence to the problems with a mixed-integer bounded set of feasible solutions and several expected value constraints. Moreover, we enable non-iid sampling and consider Holder-calmness of the constraints. We derive estimates on the sample size necessary to get a feasible solution or a lower bound on the optimal value of the original problem using the sample approximation. We present an application of the estimates to an investment problem with the Conditional Value at Risk constraints, integer allocations and transaction costs.