Local Linear Convergence of an ADMM-Type Splitting Framework for Equality Constrained Optimization  

作　　者：Jun-Feng Yang Yin Zhang 

机构地区：[1]Department of Mathematics,Nanjing University,Nanjing 210023,China [2]Institute for Data and Decision Analytics,The Chinese University of Hong Kong,Shenzhen 518172,China

出　　处：《Journal of the Operations Research Society of China》2021年第2期307-319,共13页中国运筹学会会刊（英文）

基　　金：This work was supported in part by Shenzhen Fundamental Research Fund(Nos.JCYJ-20170306141038939,KQJSCX-20170728162302784,ZDSYS-201707251409055)via the Shenzhen Research Institute of Big Data;The work of Jun-Feng Yang was supported by the National Natural Science Foundation of China(Nos.11771208,11922111,11671195).

摘　　要：We establish local convergence results for a generic algorithmic framework for solving a wide class of equality constrained optimization problems.The framework is based on applying a splitting scheme to the augmented Lagrangian function that includes as a special case the well-known alternating direction method of multipliers(ADMM).Our local convergence analysis is free of the usual restrictions on ADMM-like methods,such as convexity,block separability or linearity of constraints.It offers a much-needed theoretical justification to the widespread practice of applying ADMM-like methods to nonconvex optimization problems.

关 键 词：Alternating direction method of multipliers Nonlinear splitting Stationary iterations Spectral radius Local linear convergence 

分 类 号：O17[理学—数学]