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In this paper, we present a stochastic augmented Lagrangian approach on(possibly infinite-dimensional) Riemannian manifolds to solve stochasticoptimization problems with a finite number of deterministic constraints.Weinvestigate the convergence of the method, which is based on a stochasticapproximation approach with random stopping combined with an iterativeprocedure for updating Lagrange multipliers. The algorithm is applied to amulti-shape optimization problem with geometric constraints and demonstratednumerically.

Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds