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

• 成果类型: Article
• 署名作者: Geiersbach, Caroline; Henrion, Rene
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0177
• 发表日期: 2025
• 关键词: convex approximations; shape optimization; chance constraints

摘要

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.