Uniform Laws of Large Numbers for Set-Valued Mappings and Subdifferentials of Random Functions

Published: 2005/12/19

Stochastic Programming artstein-vitale law of large numbers, generalized gradients, random sets, sample average approximation, set-valued mappings, stochastic programming, uniform lln Short URL: https://optimization-online.org/?p=9850

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.

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