Dual Solutions in Convex Stochastic Optimization

• 成果类型: Article
• 署名作者: Pennanen, Teemu; Perkkioe, Ari-Pekka
• 署名单位: University of London; King's College London; University of Munich
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0270
• 发表日期: 2025
• 关键词: optimality conditions; DISCRETE-TIME; Recourse

摘要

This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental results in operations research, stochastic optimal control, and financial mathematics. Our analysis builds on the theory of Frechet spaces of random variables whose topological dual can be identified with the direct sum of another space of random variables and a space of singular functionals. The results are illustrated by deriving sufficient and necessary optimality conditions for several more specific problem classes. We obtain significant extensions to earlier models, for example, on stochastic optimal control, portfolio optimization, and mathematical programming.