Geometrically robust least squares through manifold optimization

Jeremy Coulson; Alberto Padoan; Cyrus Mostajeran

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arXiv · 2511.03644

Geometrically robust least squares through manifold optimization

Jeremy Coulson·Alberto Padoan·Cyrus Mostajeran

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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.

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BibTeX RIS

Jeremy Coulson, Alberto Padoan, Cyrus Mostajeran. 2025-11-05. Geometrically robust least squares through manifold optimization. https://arxiv.org/abs/2511.03644

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