Tight Convergence Rate in Subgradient Norm of the Proximal Point Algorithm

Guoyong Gu; Junfeng Yang

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arXiv · 2301.03175

Tight Convergence Rate in Subgradient Norm of the Proximal Point Algorithm

Guoyong Gu·Junfeng Yang

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Abstract

Proximal point algorithm has found many applications, and it has been playing fundamental roles in the understanding, design, and analysis of many first-order methods. In this paper, we derive the tight convergence rate in subgradient norm of the proximal point algorithm, which was conjectured by Taylor, Hendrickx and Glineur [SIAM J.~Optim., 27 (2017), pp.~1283--1313]. This sort of convergence results in terms of the residual (sub)gradient norm is particularly interesting when considering dual methods, where the dual residual gradient norm corresponds to the primal distance to feasibility.

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BibTeX RIS

Guoyong Gu, Junfeng Yang. 2023-01-09. Tight Convergence Rate in Subgradient Norm of the Proximal Point Algorithm. https://arxiv.org/abs/2301.03175

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