Corpus ID: 119308178

# Global Error Bounds and Linear Convergence for Gradient-Based Algorithms for Trend Filtering and 𝓁1-Convex Clustering

@article{Ho2019GlobalEB,
title={Global Error Bounds and Linear Convergence for Gradient-Based Algorithms for Trend Filtering and 𝓁1-Convex Clustering},
author={Nhat Ho and Tianyi Lin and Michael I. Jordan},
journal={ArXiv},
year={2019},
volume={abs/1904.07462}
}
• Nhat Ho, Tianyi Lin
• Published 2019
• Mathematics, Computer Science
• ArXiv
• We propose a class of first-order gradient-type optimization algorithms to solve structured \textit{filtering-clustering problems}, a class of problems which include trend filtering and $\ell_1$-convex clustering as special cases. Our first main result establishes the linear convergence of deterministic gradient-type algorithms despite the extreme ill-conditioning of the difference operator matrices in these problems. This convergence result is based on a convex-concave saddle point formulation… CONTINUE READING

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