- On sample average approximation for two-stage stochastic programs without relatively complete recourse Rui Chen (rchen234wisc.edu) James Luedtke (jim.luedtkewisc.edu) Abstract: We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible recourse action. As a feasibility measure of the SAA solution, we consider the recourse likelihood'', which is the probability that the solution has a feasible recourse action. For $\epsilon \in (0,1)$, we demonstrate that the probability that a SAA solution has recourse likelihood below $1-\epsilon$ converges to zero exponentially fast with the sample size. Next, we analyze the rate of convergence of optimal solutions of the SAA to optimal solutions of the true problem for problems with a finite feasible region, such as bounded integer programming problems. For problems with non-finite feasible region, we propose modified padded'' SAA problems and demonstrate in two cases that such problems can yield, with high confidence, solutions that are certain to have a feasible recourse decision. Finally, we conduct a numerical study on a two-stage resource planning problem that illustrates the results, and also suggests there may be room for improvement in some of the theoretical analysis. Keywords: Stochastic programming, Mixed-integer programming, Sample average approximation, Chance constraints Category 1: Stochastic Programming Citation: Chen, Rui, and James Luedtke. "On sample average approximation for two-stage stochastic programs without relatively complete recourse." Mathematical Programming (2022): 1-36. Download: Entry Submitted: 12/30/2019Entry Accepted: 12/31/2019Entry Last Modified: 01/20/2022Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.