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Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds

Author

Listed:
  • Caroline Geiersbach

    (Weierstrass Institute)

  • Tim Suchan

    (Helmut Schmidt University/University of the Federal Armed Forces Hamburg)

  • Kathrin Welker

    (TU Bergakademie Freiberg)

Abstract

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.

Suggested Citation

  • Caroline Geiersbach & Tim Suchan & Kathrin Welker, 2024. "Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 165-195, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02488-1
    DOI: 10.1007/s10957-024-02488-1
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    References listed on IDEAS

    as
    1. Veronika Karl & Daniel Wachsmuth, 2018. "An augmented Lagrange method for elliptic state constrained optimal control problems," Computational Optimization and Applications, Springer, vol. 69(3), pages 857-880, April.
    2. Yuya Yamakawa & Hiroyuki Sato, 2022. "Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method," Computational Optimization and Applications, Springer, vol. 81(2), pages 397-421, March.
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