Tight Convergence Rate in Subgradient Norm of the Proximal Point Algorithm

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 Ta...

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Hauptverfasser:	Gu, Guoyong, Yang, Junfeng
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Schlagworte:	Mathematics - Optimization and Control
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creator	Gu, Guoyong Yang, Junfeng
description	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.
doi_str_mv	10.48550/arxiv.2301.03175
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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]. 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title	Tight Convergence Rate in Subgradient Norm of the Proximal Point Algorithm
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