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

Alexander Shapiro (ashapiroisye.gatech.edu)
Huifu Xu (h.xumaths.soton.ac.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

Category 1: Stochastic Programming

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Entry Submitted: 12/19/2005
Entry Accepted: 12/19/2005
Entry Last Modified: 12/19/2005

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