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https://dx.doi.org/10.48550/ar...
Article . 2024
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A Decentralized Proximal Gradient Tracking Algorithm for Composite Optimization on Riemannian Manifolds

Authors: Wang, Lei; Bao, Le; Liu, Xin;

A Decentralized Proximal Gradient Tracking Algorithm for Composite Optimization on Riemannian Manifolds

Abstract

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches at present for tackling such composite optimization problems. The first, subgradient-based approaches, rely on subgradient information of the objective function to update variables, achieving an iteration complexity of $\mathcal{O}(ε^{-4}\log^2(ε^{-2}))$. The second, smoothing approaches, involve constructing a smooth approximation of the nonsmooth regularization term, resulting in an iteration complexity of $\mathcal{O}(ε^{-4})$. This paper proposes a proximal gradient type algorithm that fully exploits the composite structure. The global convergence to a stationary point is established with a significantly improved iteration complexity of $\mathcal{O}(ε^{-2})$. To validate the effectiveness and efficiency of our proposed method, we present numerical results in real-world applications, showcasing its superior performance.

Keywords

Optimization and Control (math.OC), Optimization and Control, FOS: Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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