Work

Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds

Year: 2024

Type: article

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.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-024-02488-1

Authors: Caroline Geiersbach, Tim Suchan, Kathrin Welker

Institutions: Weierstrass Institute for Applied Analysis and Stochastics, Helmut Schmidt University, TU Bergakademie Freiberg

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: European Commission, Deutsche Forschungsgemeinschaft