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Set-Valued and Variational Analysis

, Volume 26, Issue 4, pp 821–841 | Cite as

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

  • M. H. Farshbaf-Shaker
  • R. HenrionEmail author
  • D. Hömberg
Article

Abstract

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.

Keywords

Chance constraints Probabilistic constraints PDE constrained optimization 

Mathematics Subject Classifications (2010)

90C15 49J20 

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Notes

Acknowledgments

The authors express their gratitude to two anonymous referees whose very careful reading and critical comments led to a substantially improved presentation of this paper.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • M. H. Farshbaf-Shaker
    • 1
  • R. Henrion
    • 1
    Email author
  • D. Hömberg
    • 1
    • 2
  1. 1.Weierstrass InstituteBerlinGermany
  2. 2.Department of Mathematical SciencesNTNUTrondheimNorway

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