非光滑分布式优化的近端跟踪线性收敛速率分析
Linear convergence rate analysis of Proximal-Tracking for nonsmooth distributed optimization
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中文总结 AI 辅助
本文针对非光滑分布式优化中的近端跟踪算法，在强凸性和平静性假设下证明了其线性收敛速率，且无需可微性假设，保留了算法优势。
中文摘要 AI 辅助
近端跟踪（Proximal-Tracking）是一种新颖的算法，由Falsone和Prandini在Automatica, 135 (2022), 109938中提出，用于解决具有局部集合约束的非光滑分布式共识优化问题。该算法的全局收敛性和数值行为已在上述文献中得到充分研究。作为补充，本文在额外强凸性和平静性假设下，对其线性收敛速率进行了理论分析。特别地，该分析不需要可微性或光滑性等假设，从而保留了算法的原有优势。
英文摘要
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.
发表机构
- School of Mathematical Sciences, Dalian University of Technology（大连理工大学数学科学学院）
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