Optimality Conditions for Convex Stochastic Optimization Problems in Banach Spaces with Almost Sure State Constraints

We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessar...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Geiersbach, Caroline, Wollner, Winnifried
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 28.06.2021
Subjects:
Banach spaces
Constraints
Lagrange multiplier
Optimization
Random variables
ISSN:2331-8422
Online Access:Get full text
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Summary:We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessary and sufficient. Additionally, the Lagrange multipliers associated with optimality conditions are integrable vector-valued functions and not only measures. A model problem is given demonstrating the application to PDE-constrained optimization under uncertainty with an outlook for further applications.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2009.04168