On the linear convergence rate of the generalized proximal point algorithm
Fixed Point Methods and Optimization, Volume 2, Issue 2, August 2025, Pages 158–166
NA XIAN
Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province, School of Mathematics and Information, China West Normal University, Nanchong 637009, China
KE GUO
Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province, School of Mathematics and Information, China West Normal University, Nanchong 637009, China
Abstract
The proximal point algorithm (PPA) has been extensively studied in the literature, with its linear convergence rate well established. Recent studies have demonstrated that PPA retains linear convergence under specific regularity conditions, including subdifferential error bound, the Polyak–Łojasiewicz inequality, and quadratic growth. The generalized proximal point algorithm (GPPA), a relaxed variant of PPA, offers numerical acceleration compared to the classical scheme. In this paper, we focus on examining the linear convergence of GPPA under the same regularity conditions that apply to PPA.
Cite this Article as
Na Xian and Ke Guo, On the linear convergence rate of the generalized proximal point algorithm, Fixed Point Methods and Optimization, 2(2), 158–166, 2025