Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds

Caroline Geiersbach (), Tim Suchan () and Kathrin Welker ()
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Caroline Geiersbach: Weierstrass Institute
Tim Suchan: Helmut Schmidt University/University of the Federal Armed Forces Hamburg
Kathrin Welker: TU Bergakademie Freiberg

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 8, 165-195

Abstract: 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.

Keywords: Augmented Lagrangian; Stochastic optimization; Uncertainties; Inequality constraints; Riemannian manifold; Shape optimization; Geometric constraints; 49Q10; 60H35; 35R15; 49K20; 41A25; 60H15; 60H30; 35R60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02488-1

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