Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds
Optimization and Control
2025-04-01 v2
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.
Cite
@article{arxiv.2303.17404,
title = {Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds},
author = {Caroline Geiersbach and Tim Suchan and Kathrin Welker},
journal= {arXiv preprint arXiv:2303.17404},
year = {2025}
}