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Optimality conditions in control problems with random state constraints in probabilistic or almost-sure form

Submission Status:revision under review
  • In this paper, we discuss optimality conditions for optimization problems {involving} random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation (PDE) with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian random vectors in order to formulate fully explicit optimality conditions involving a spherical integral. In the almost sure case, we derive optimality conditions and compare them to a model based on robust constraints with respect to the (compact) support of the given distribution.

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Author:Caroline Geiersbach, René Henrion
Document Type:Article
Date of Publication (online):2024/01/15
Release Date:2024/01/15
Licence (German):License LogoCreative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International