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Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions

Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions
Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions
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.
0022-247X
1390-1399
Shapiro, Alexander
c17bba20-6f82-47be-b8a3-859504691942
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Shapiro, Alexander
c17bba20-6f82-47be-b8a3-859504691942
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Shapiro, Alexander and Xu, Huifu (2007) Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions. Journal of Mathematical Analysis and Applications, 325, 1390-1399. (doi:10.1016/j.jmaa.2006.02.078).

Record type: Article

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.

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More information

Published date: 2007
Organisations: Operational Research

Identifiers

Local EPrints ID: 79544
URI: http://eprints.soton.ac.uk/id/eprint/79544
ISSN: 0022-247X
PURE UUID: 884e782e-c821-4249-9e75-cef4f61637e2
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 17 Mar 2010
Last modified: 14 Mar 2024 02:47

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Contributors

Author: Alexander Shapiro
Author: Huifu Xu ORCID iD

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