Optimality Conditions for Convex Stochastic Optimization Problems in Banach Spaces with Almost Sure State Constraints
Copyright policy )Optimality Conditions for Convex Stochastic Optimization Problems in Banach Spaces with Almost Sure State Constraints
We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessary and sufficient. Additionally, the Lagrange multipliers associated with optimality conditions are integrable vector-valued functions and not only measures. A model problem is given demonstrating the application to PDE-constrained optimization under uncertainty.
- Leibniz Association Germany
- Weierstrass Institute Germany
- Weierstrass Institute for Applied Analysis and Stochastics Germany
- Technische Universität Darmstradt Germany
- TU Darmstadt Germany
regular Lagrange multipliers, PDE-constrained optimization under uncertainty -- optimization in Banach spaces -- optimality conditions -- convex stochastic optimization in Banach spaces -- two-stage stochastic optimization -- regular Lagrange multipliers -- duality, 49N15, Stochastic programming, two-stage stochastic optimization, optimization in Banach spaces, convex stochastic optimization, 510, PDE-constrained optimization under uncertainty, convex stochastic optimization in Banach spaces, FOS: Mathematics, 49K21, 49K45, Duality theory (optimization), Mathematics - Optimization and Control, 49K20, ddc:510, Optimality conditions, optimality conditions, article, stochastic optimization problems in abstract spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, Optimization and Control (math.OC), duality, 49J53
regular Lagrange multipliers, PDE-constrained optimization under uncertainty -- optimization in Banach spaces -- optimality conditions -- convex stochastic optimization in Banach spaces -- two-stage stochastic optimization -- regular Lagrange multipliers -- duality, 49N15, Stochastic programming, two-stage stochastic optimization, optimization in Banach spaces, convex stochastic optimization, 510, PDE-constrained optimization under uncertainty, convex stochastic optimization in Banach spaces, FOS: Mathematics, 49K21, 49K45, Duality theory (optimization), Mathematics - Optimization and Control, 49K20, ddc:510, Optimality conditions, optimality conditions, article, stochastic optimization problems in abstract spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, Optimization and Control (math.OC), duality, 49J53
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!