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Proximal point algorithm has found many applications, and it has been playingfundamental roles in the understanding, design, and analysis of manyfirst-order methods. In this paper, we derive the tight convergence rate insubgradient norm of the proximal point algorithm, which was conjectured byTaylor, Hendrickx and Glineur [SIAM J.~Optim., 27 (2017), pp.~1283--1313]. Thissort of convergence results in terms of the residual (sub)gradient norm isparticularly interesting when considering dual methods, where the dual residualgradient norm corresponds to the primal distance to feasibility.

Tight Convergence Rate in Subgradient Norm of the Proximal Point Algorithm