Dual Solutions in Convex Stochastic Optimization

Teemu Pennanen () and Ari-Pekka Perkkiö ()
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Teemu Pennanen: Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom
Ari-Pekka Perkkiö: Mathematics Institute, Ludwig Maximilian University of Munich, 80333 Munich, Germany

Mathematics of Operations Research, 2025, vol. 50, issue 3, 2375-2404

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.

Keywords: 46N10; 90C15; 90C46; 93E20; stochastic programming; convexity; duality; optimality conditions (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:2375-2404

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