  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.
