WIAS Preprint No. 2862, (2021)

Optimality conditions and Moreau--Yosida regularization for almost sure state constraints


  • Geiersbach, Caroline
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479

2020 Mathematics Subject Classification

  • 49K20 49K45 49N15 49J20 90C15


  • PDE-constrained optimization under uncertainty, optimization in Banach spaces, optimality conditions, regularization, convex stochastic optimization in Banach spaces, two-stages stochastic optimization, duality




We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable. We obtain strong forms of necessary and sufficient optimality conditions for problems subject to equality and conical constraints. We propose a Moreau--Yosida regularization for the conical constraint and show consistency of the optimality conditions for the regularized problem as the regularization parameter is taken to infinity.

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