A reduction framework converts unconstrained optimized first-order methods into composite-setting methods with analogous rates, yielding new proximal OGM and proximal OGM-G guarantees.
Tight Convergence Rate in Subgradient Norm of the Proximal Point Algorithm
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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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Optimized methods for composite optimization: a reduction perspective
A reduction framework converts unconstrained optimized first-order methods into composite-setting methods with analogous rates, yielding new proximal OGM and proximal OGM-G guarantees.