Dynamic probabilistic constraints under continuous random distributions

• 成果类型: Article
• 署名作者: Gonzalez Grandon, T.; Henrion, R.; Perez-Aros, P.
• 署名单位: Humboldt University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Universidad de O'Higgins
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01593-z
• 发表日期: 2022
• 页码: 1065-1096
• 关键词: chance constraints; optimization

摘要

The paper investigates analytical properties of dynamic probabilistic constraints (chance constraints). The underlying random distribution is supposed to be continuous. In the first part, a general multistage model with decision rules depending on past observations of the random process is analyzed. Basic properties like (weak sequential) (semi-) continuity of the probability function or existence of solutions are studied. It turns out that the results differ significantly according to whether decision rules are embedded into Lebesgue or Sobolev spaces. In the second part, the simplest meaningful two-stage model with decision rules from L-2 is investigated. More specific properties like Lipschitz continuity and differentiability of the probability function are considered. Explicitly verifiable conditions for these properties are provided along with explicit gradient formulae in the Gaussian case. The application of such formulae in the context of necessary optimality conditions is discussed and a concrete identification of solutions presented.