Geometrically robust least squares through manifold optimization

2025/11/05 by Coulson, Jeremy, Padoan, Alberto, Mostajeran, Cyrus · 1 citation
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2511.03644

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.

Citations

• Simple algorithms for optimization on Riemannian manifolds with constraints
• Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation
• Online Identification and Tracking of Subspaces from Highly Incomplete\n Information

Cited by

• Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach

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