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Approximating stationary points of stochastic optimization problems in Banach space

Approximating stationary points of stochastic optimization problems in Banach space
Approximating stationary points of stochastic optimization problems in Banach space
In this paper, we present a uniform strong law of large numbers for random set-valued mappings in separable Banach space and apply it to analyze the sample average approximation of Clarke stationary points of a nonsmooth one stage stochastic minimization problem in separable Banach space. Moreover, under Hausdorff continuity, we show that with probability approaching one exponentially fast with the increase of sample size, the sample average of a convex compact set-valued mapping converges to its expected value uniformly. The result is used to establish exponential convergence of stationary sequence under some metric regularity conditions.
0022-247X
333-343
Balaji, Ramamurthy
fb02ef7d-e528-40df-9128-7c217af0b4ca
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Balaji, Ramamurthy
fb02ef7d-e528-40df-9128-7c217af0b4ca
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Balaji, Ramamurthy and Xu, Huifu (2008) Approximating stationary points of stochastic optimization problems in Banach space. Journal of Mathematical Analysis and Applications, 347 (1), 333-343. (doi:10.1016/j.jmaa.2008.06.015).

Record type: Article

Abstract

In this paper, we present a uniform strong law of large numbers for random set-valued mappings in separable Banach space and apply it to analyze the sample average approximation of Clarke stationary points of a nonsmooth one stage stochastic minimization problem in separable Banach space. Moreover, under Hausdorff continuity, we show that with probability approaching one exponentially fast with the increase of sample size, the sample average of a convex compact set-valued mapping converges to its expected value uniformly. The result is used to establish exponential convergence of stationary sequence under some metric regularity conditions.

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More information

Published date: 2008
Organisations: Operational Research

Identifiers

Local EPrints ID: 54139
URI: https://eprints.soton.ac.uk/id/eprint/54139
ISSN: 0022-247X
PURE UUID: 04e12460-0526-4181-bda3-af916415d627

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Date deposited: 17 Mar 2010
Last modified: 13 Mar 2019 20:39

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