On Iteration Complexity of a First-Order Primal-Dual Method for Nonlinear Convex Cone Programming

作     者：Lei Zhao Dao-Li Zhu 

作者机构：School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China Antai College of Economics and Management and Sino-US Global Logistics InstituteShanghai Jiao Tong UniversityShanghai 200230China School of Data ScienceThe Chinese University of Hong KongShenzhen 518172GuangdongChina 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2022年第10卷第1期

页      面：53-87页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：This research was supported by the National Natural Science Foundation of China(Nos.71471112 and 71871140) 

主　　题：Nonlinear convex cone programming First-order method Primal-dual method Augmented Lagrangian function 

摘      要：Nonlinear convex cone programming(NCCP)models have found many practical *** this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for solving NCCP problems when the objective function and constraints are convex but may be *** each iteration,VAPP generates a nonlinear approximation of the primal augmented Lagrangian *** approximation incorporates both linearization and a distance-like proximal term,and then the iterations of VAPP are shown to possess a decomposition property for *** by recent applications in big data analytics,there has been a growing interest in the convergence rate analysis of algorithms with parallel computing capabilities for large scale optimization *** establish O(1/t)convergence rate towards primal optimality,feasibility and dual *** adaptively setting parameters at different iterations,we show an O(1/t2)rate for the strongly convex ***,we discuss some issues in the implementation of VAPP.