Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form

Caroline Geiersbach () and René Henrion ()
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Caroline Geiersbach: Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany
René Henrion: Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany

Mathematics of Operations Research, 2025, vol. 50, issue 3, 1654-1680

Abstract: In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. Although 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 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 with a model based on robust constraints with respect to the (compact) support of the given distribution.

Keywords: Primary: 49K20; 49K45; 35Q93; 49J52; 90C15; optimality conditions; stochastic optimization; PDE-constrained optimization under uncertainty; chance constraints; almost sure constraints; robust constraints (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:3:p:1654-1680

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