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

• Published in: Set-valued and variational analysis Vol. 26; no. 4; pp. 821 - 841
• Main Authors: Farshbaf-Shaker, M. H., Henrion, R., Hömberg, D.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2018; Springer Nature B.V
• Subjects: Analysis; Constraints; Continuity; Convexity; Dimensional stability; Mathematics; Mathematics and Statistics; Optimization; Parameter uncertainty; Chance constraints; 90C15; Probabilistic constraints; 49J20; PDE constrained optimization
• ISSN: 1877-0533; 1877-0541
• DOI: 10.1007/s11228-017-0452-5

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.