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Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions |
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| Authors: | Alexander Shapiro Huifu Xu |
| Institution: | a School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA b School of Mathematics, University of Southampton, Highfield Southampton, SO17 1BJ, UK |
| Abstract: | We derive a uniform (strong) Law of Large Numbers (LLN) for random set-valued mappings. The result can be viewed as an extension of both, a uniform LLN for random functions and LLN for random sets. We apply the established results to a consistency analysis of stationary points of sample average approximations of nonsmooth stochastic programs. |
| Keywords: | Random sets Artstein-Vitale law of large numbers Set-valued mappings Uniform LLN Generalized gradients Stochastic programming Sample average approximation |
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