Decentralized Non-Smooth Optimization Over the Stiefel Manifold

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of many agents cooperatively mini-mize a finite-sum objective function with each component being weakly convex in the ambient Euclidean space. Such optimization p...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop pp. 1 - 5
Main Authors Wang, Jinxin, Hu, Jiang, Chen, Shixiang, Deng, Zengde, So, Anthony Man-Cho
Format Conference Proceeding
LanguageEnglish
Published IEEE 08.07.2024
Subjects
Array signal processing
Conferences
decentralized non-smooth optimization
Gradient methods
Iterative methods
Linear programming
Manifolds
Optimization
Riemannian sub gradient method
sharpness
Stiefel manifold
Online AccessGet full text

Cover

More Information
Summary:We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of many agents cooperatively mini-mize a finite-sum objective function with each component being weakly convex in the ambient Euclidean space. Such optimization problems, albeit frequently encountered in applications, are quite challenging due to their non-smoothness and non-convexity. To tackle them, we propose an iterative method called the decentralized Riemannian sub gradient method (DRSM). When the problem at hand possesses a sharpness property, we show the local linear convergence of DRSM using geometrically di-minishing stepsizes. Numerical experiments are conducted to demonstrate the superior performance of DRSM in different applications.
ISSN:2151-870X
DOI:10.1109/SAM60225.2024.10636572