WIAS Preprint No. 3010, (2023)

Stochastic augmented Lagrangian method in shape spaces


  • Geiersbach, Caroline
    ORCID: 0000-0002-6518-7756
  • Suchan, Tim
  • Welker, Kathrin

2020 Mathematics Subject Classification

  • 49Q10 60H35 35R15 49K20 41A25 60H15 60H30 35R60


  • augmented Lagrangian, stochastic optimization, uncertainties, inequality constraints, Riemannian manifold, shape optimization, geometric constraints




In this paper, we present a stochastic Augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically.

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