An LQP-Based Symmetric Alternating Direction Method of Multipliers with Larger Step Sizes  

作　　者：Zhong-Ming Wu Min Li 

机构地区：[1]School of Economics and Management,Southeast University,Nanjing 210096,China [2]School of Management and Engineering,Nanjing University,Nanjing 210093,China

出　　处：《Journal of the Operations Research Society of China》2019年第2期365-383,共19页中国运筹学会会刊（英文）

基　　金：This research was supported by National Natural Science Foundation of China Grant 11771078;Natural Science Foundation of Jiangsu Province Grant BK20181258;Project of 333 of Jiangsu Province Grant BRA2018351;Postgraduate Research&Practice Innovation Program of Jiangsu Province Grant KYCX18_0200.

摘　　要：Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.

关 键 词：Convex optimization Symmetric alternating direction method of multipliers Logarithmic-quadratic proximal regularization Larger step sizes Global convergence 

分 类 号：O17[理学—数学]