Adaptive Parallel Primal-Dual Method for Saddle Point Problems

作     者：Xiayang Zhang 

作者机构：Department of MathematicsNanjing UniversityNanjing210093China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2018年第11卷第1期

页      面：187-210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 is supported by National Natural Science Foundation of China(Nos.71201080,71571096) Social Science Foundation of Jiang-su Province(No.14GLC001) Fundamental Research Funds for the Central Universities(No.020314380016) 

主　　题：Adaptive Parallel Primal-dual method Saddle-point problem LASSO 

摘      要：The primal-dual hybrid gradient method is a classic way to tackle saddle-point ***,its convergence is not guaranteed in *** restric-tions on the step size parameters,e.g.,τσ≤1/||A^(T)A||,are imposed to guarantee the *** this paper,a new convergent method with no restriction on parame-ters is *** the expensive calculation of ||A^(T)A|| is *** method produces a predictor like other primal-dual methods but in a parallel fashion,which has the potential to speed up the *** new iterate is then updated by a sim-ple correction to guarantee the ***,the parameters are adjusted dynamically to enhance the efficiency as well as the robustness of the *** generated sequence monotonically converges to the solution set.A worst-case O(1/t)convergence rate in ergodic sense is also established under mild *** nu-merical efficiency of the proposed method is verified by applications in LASSO problem and Steiner tree problem.