TY - JOUR A1 - Farshbaf-Shaker, M. Hassan A1 - Henrion, Rene A1 - Hömberg, Dietmar T1 - Properties of Chance Constraints in Infinite Dimensions with an Application to PDE Constrained Optimization JF - Set-Valued and Variational Analysis N2 - 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. KW - Chance constraints KW - Probabilistic constraints KW - PDE constrained optimization Y1 - 2018 U6 - https://doi.org/doi:10.1007/s11228-017-0452-5 ER -