Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/313373 
Authors: 
Year of Publication: 
2022
Citation: 
[Journal:] Optimization Letters [ISSN:] 1862-4480 [Volume:] 17 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 471-492
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
We analyze the tail behavior of solutions to sample average approximations (SAAs) of stochastic programs posed in Hilbert spaces. We require that the integrand be strongly convex with the same convexity parameter for each realization. Combined with a standard condition from the literature on stochastic programming, we establish non-asymptotic exponential tail bounds for the distance between the SAA solutions and the stochastic program’s solution, without assuming compactness of the feasible set. Our assumptions are verified on a class of infinite-dimensional optimization problems governed by affine-linear partial differential equations with random inputs. We present numerical results illustrating our theoretical findings.
Subjects: 
Sample average approximation
PDE-constrained optimization under uncertainty
Linear-quadratic optimal control under uncertainty
Exponential tail bounds
Stochastic programming
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.