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Linear convergence rate analysis of Proximal-Tracking for nonsmooth distributed optimization

  • Tianyu Yuan
  • Xiantao Xiao
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Abstract

Proximal-Tracking is a novel algorithm proposed in [Falsone and Prandini, Automatica, 135 (2022), 109938] for nonsmooth distributed consensus optimization with local set constraints. The global convergence and numerical behavior of Proximal-Tracking have been well studied in [Falsone and Prandini, Automatica, 135 (2022), 109938]. As a complement, in this paper we provide a theoretical analysis regarding its linear convergence rate under additional strong convexity and calmness assumptions. In particular, this analysis does not require assumptions such as differentiability or smoothness, thus preserving the original advantages of the algorithm.

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Cite

BibTeXRIS
BibTeX
@misc{yuan2026linear,
  title = {{Linear convergence rate analysis of Proximal-Tracking for nonsmooth distributed optimization}},
  author = {Tianyu Yuan and Xiantao Xiao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27400},
  eprint = {2609.27400},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27400},
}
RIS
TY  - UNPB
TI  - Linear convergence rate analysis of Proximal-Tracking for nonsmooth distributed optimization
AU  - Tianyu Yuan
AU  - Xiantao Xiao
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27400
UR  - https://arxiv.org/abs/2609.27400
AB  - Proximal-Tracking is a novel algorithm proposed in [Falsone and Prandini, Automatica, 135 (2022), 109938] for nonsmooth distributed consensus optimization with local set constraints. The global convergence and numerical behavior of Proximal-Tracking have been well studied in [Falsone and Prandini, Automatica, 135 (2022), 109938]. As a complement, in this paper we provide a theoretical analysis regarding its linear convergence rate under additional strong convexity and calmness assumptions. In particular, this analysis does not require assumptions such as differentiability or smoothness, thus preserving the original advantages of the algorithm.
ER  -