A New Perspective of Proximal Gradient Algorithms

Yi Zhou, Yingbin Liang, Lixin Shen

Published 2015-03-18Version 1

We take a di?erent approach to analyze the generalized proximal point algorithm (GPPA). Our analysis justi?es the structure imposed on the distance metric in establishing the convergence rate of GPPA.We then show that both proximal gradient algorithm (PGA) and Bregman proximal gradient algorithm (BPGA) can be viewed as GPPA, based on which the convergence rates of PGA and BPGA are obtained directly. Furthermore, the convergence rate obtained in this way is more accurate than the existing rate.