Dual Solutions in Convex Stochastic Optimization

Pennanen, Teemu und Perkkiö, Ari-Pekka (12. September 2024): Dual Solutions in Convex Stochastic Optimization. In: Mathematics of Operations Research [Forthcoming]

Abstract

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 Fréchet 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0364-765X
• Sprache: Englisch