The problem of finding a zero point of a maximal monotone operator plays a central role in modeling many application problems arising from various fields,and the proximal point algorithm(PPA)is among the fundamental a...The problem of finding a zero point of a maximal monotone operator plays a central role in modeling many application problems arising from various fields,and the proximal point algorithm(PPA)is among the fundamental algorithms for solving the zero-finding problem.PPA not only provides a very general framework of analyzing convergence and rate of convergence of many algorithms,but also can be very efficient in solving some structured problems.In this paper,we give a survey on the developments of PPA and its variants,including the recent results with linear proximal term,with the nonlinear proximal term,as well as the inexact forms with various approximate criteria.展开更多
基金Xing-Ju Cai and Fan Jiang were supported by the National Natural Science Foundation of China(Nos.11871279 and 11571178)Ke Guo was supported by the National Natural Science Foundation of China(Nos.11801455,11871059 and 11971238)+8 种基金China Postdoctoral Science Foundation(Nos.2019M663459 and 2020T130081)the Applied Basic Project of Sichuan Province(No.2020YJ0111)the Fundamental Research Funds of China West Normal University(No.18B031)the Open Project of Key Laboratory(No.CSSXKFKTM202004)School of Mathematical Sciences,Chongqing Normal University.Kai Wang was supported by the National Natural Science Foundation of China(No.11901294)Natural Science Foundation of Jiangsu Province(No.BK20190429)Zhong-Ming Wu was supported by the National Natural Science Foundation of China(No.12001286)the Startup Foundation for Introducing Talent of NUIST(No.2020r003)De-Ren Han was supported by the National Natural Science Foundation of China(Nos.12131004 and 12126603)。
文摘The problem of finding a zero point of a maximal monotone operator plays a central role in modeling many application problems arising from various fields,and the proximal point algorithm(PPA)is among the fundamental algorithms for solving the zero-finding problem.PPA not only provides a very general framework of analyzing convergence and rate of convergence of many algorithms,but also can be very efficient in solving some structured problems.In this paper,we give a survey on the developments of PPA and its variants,including the recent results with linear proximal term,with the nonlinear proximal term,as well as the inexact forms with various approximate criteria.
