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Properties of Chance Constraints in Infinite Dimensions with an Application to PDE Constrained Optimization

Submission Status:accepted for publication
  • Chance constraints represent a popular tool for finding decisions that enforce the satisfaction of random inequality systems in terms of probability. They are widely used in optimization problems subject to uncertain parameters as they arise in many engineering applications. Most structural results of chance constraints (e.g., closedness, convexity, Lipschitz continuity, differentiability etc.) have been formulated in finite dimensions. The aim of this paper is to generalize some of these well-known semi-continuity and convexity properties as well as a stability result to an infinite dimensional setting. The abstract results are applied to a simple PDE constrained control problem subject to (uniform) state chance constraints.

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Metadaten
Author:M. Hassan Farshbaf-Shaker, Rene Henrion, Dietmar Hömberg
DOI:https://doi.org/doi:10.1007/s11228-017-0452-5
Parent Title (English):Set-Valued and Variational Analysis
Document Type:Article
Language:English
Date of Publication (online):2018/05/01
Date of first Publication:2018/01/09
Release Date:2018/01/09
Tag:Chance constraints; PDE constrained optimization; Probabilistic constraints
Institutes:Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B04