Geometrically robust least squares through manifold optimization
Abstract
This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization problem on a product manifold, where one variable is constrained to a ball describing uncertainty. To handle the constraint, an exact penalty method is applied. A first-order gradient descent ascent algorithm is proposed to solve the problem, and its convergence properties are illustrated by an example. The proposed method offers a robust approach to solving a wide range of problems arising in signal processing and data-driven control.
Cite
@article{arxiv.2511.03644,
title = {Geometrically robust least squares through manifold optimization},
author = {Jeremy Coulson and Alberto Padoan and Cyrus Mostajeran},
journal= {arXiv preprint arXiv:2511.03644},
year = {2025}
}
Comments
Submitted to the 26th International Symposium on Mathematical Theory of Networks and Systems 19-23 August 2024, Cambridge, UK