Professor Bingsheng He

 

 

 

 

 

 

 

 

 

 

 

Department of Mathematics, SUSTech

(Southern University of Science and Technology),

Shenzhen, 518055, China  

Phone: +86-755-88018721   Email: hebs@sustech.edu.cn

&

Department of Mathematics,

Nanjing University, Nanjing, 210093,  China

E-mail: hebma@nju.edu.cn

 

Current Research Areas:

Mathematical Programming,  Numerical Optimization,  Variational Inequalities,

ADMM-like splitting contraction methods for convex optimization

 

Education:

PhD: Applied Mathematics, The University of Wuerzburg, Germany, 1986

Thesis Advisor: Professor Dr. Josef Stoer

BSc: Computational Mathematics, Nanjing University, 1981

 

Work:

    2015---        Professor, Dept. of Math, Southern University of Science and Technology (SUSTech)

    2013-2015   Professor,  School of Management Science and Engineering, Nanjing University

1997~2013   Professor, Department of Mathematics, Nanjing University

1992~1997  Associate Professor, Department of Mathematics,Nanjing University

 


      Supervised Students


      我的几类主要研究工作的分类论文和简要介绍(附阅读建议)

   1. 变分不等式的投影收缩算法(Projection-Contraction Methods)      2. 两个可分离函数的乘子交替方向法(ADMM)

        3. 多个可分离函数的交替方向类算法(ADMM-Like Methods)         4. 变分不等式框架下的邻近点算法(VI & PPA)


 

     My Thinkings:

     1.   关门感想          2.  说说我的主要研究兴趣 — 兼谈华罗庚推广优选法对我的影响 

                                             3.  说说我的主要研究兴趣(续)  --- 我们在ADMM类方法的主要工作

      4.  古稀回首          5.  两页纸简述我职业生涯中的主要研究工作        


     My Talks:

       1. 从变分不等式的投影收缩算法到凸规划的分裂收缩算法 —  我研究生涯的来龙去脉

     2. 生活理念对设计优化分裂算法的帮助 以改造 ADMM 求解三个可分离算子问题为例

     3. 凸优化的分裂收缩算法 — 变分不等式为工具的统一框架      (适合打印的 综合文本)

      4. 从商业谈判的角度看一些优化方法的设计  —  从 min-max 问题的求解谈起

       5. 乘子交替方向法(ADMM) 的20年 —  2017 年5月全国数学规划会议报告   综述版本

     6.图像处理中的凸优化问题及其相应的分裂收缩算法 — ISICDM会议报告I    报告II   报告III  

     7.介绍:构造求解凸优化的分裂收缩算法用好变分不等式和邻近点算法两大法宝  

     8.线性化ALM-ADMM等方法“替代”参数严重影响收敛速度提升空间有多少?  

     9.被 S. Becker 誉为 Very Simple yet Powerful Technique 的主要思想-应用及新的进展


     My Foundations:                                                                                    

       1. 国家自然科学基金    2 教育部博士点基金---江苏省自然科学基金        我喜欢用大黑板(小视频)


 

       凸优化和单调变分不等式的分裂收缩算法  (2019年旧版)

 

                                           统一框架与应用 -- 算法研究力求数学之美

 

            前言、目录、阅读建议和各讲提要

 

              第一部分:单调变分不等式的求解方法

 

                     第1讲.    变分不等式作为多种问题的统一表述模式

 

                     第2讲.    三个基本不等式和变分不等式的投影收缩算法

 

                     第3讲.   单调变分不等式投影收缩算法中的两对孪生方法    

 

                     第4讲.    线性变分不等式投影收缩算法的收敛速率   

            

                     第5讲.    非线性变分不等式投影收缩算法的收敛速率

 

              第二部分:凸优化问题{min f(x)| Ax=b, x in X}的求解方法

 

                     第6讲.    为线性约束凸优化问题定制的PPA算法及其应用

 

                     第7讲.    线性约束凸优化问题基于松弛PPA的收缩算法

 

                     第8讲.    线性约束凸优化扩展问题的PPA和松弛PPA收缩算法

 

                     第9讲.    基于增广 Lagrange 乘子法的PPA收缩算法

 

                     第10讲.  基于梯度投影的凸优化收缩算法和下降算法

 

              第三部分:凸优化问题{min f(x)+g(y)| Ax + By=b, x in X, y in Y}的交替方向法

 

                    第11讲.   结构型优化的交替方向法(ADMM)

 

                    第12讲.   线性化的交替方向收缩算法

 

                    第13讲.   定制 PPA 意义下的交替方向法及其线性化方法

 

                    第14讲.   自变量 x-y 地位相等的对称型交替方向法 

  

                    第15讲.   交替方向法遍历和点列意义的收敛速率

 

              第四部分:多块可分离凸优化问题的 ADMM 类分裂收缩算法

 

                    第16讲.   三块可分离凸优化问题的平行分裂增广Lagrange乘子法

 

                    第17讲.   三块可分离凸优化问题的略有改动的交替分向法


                    第18讲.   多块可分离凸优化问题带高斯回代的交替方向法


                    第19讲.   多块可分离凸优化问题部分平行加正则化 的交替方向法

 

                    第20讲.  变分不等式意义下凸优化分裂收缩算法的统一框架

 


   Lectures of  'Contraction Methods for Convex Optimization and Monotone Variational Inequalities' 

 

       Working Papers   (Some of recent research manuscripts are included.)

 


 

     Publications:      

 

     1. B.S. He,  F. Ma and X.M. Yuan,  Optimal proximal augmented Lagrangian method and its application to full Jacobian

          splitting for multi-block separable convex minimization problems, IMA Journal of Numerical  Analysis. 39(2019).

     2  B.S. HeM.H. Xu and X.M. Yuan, Block-wise ADMM with a relaxation factor for multiple-block convex programming. 

         J. Oper. Res. Soc. China 6 (2018), 485–505. 

     3. B. S. He, My 20 years research on alternating directions method of multipliers. (Chinese) Oper. Res. Trans. 22 (2018), 1–31.    

     4. B.S. He, and X. M. Yuan, A class of ADMM-based algorithms for three-block separable convex programming.

           Comput. Optim. Appl. 70 (2018), 791–826.

     5. B. S He, A uniform framework of contraction methods for convex optimization and monotone variational inequality. (Chinese)

         Scientia Sinica Mathematica 48 (2018)  255-272

     6. B.S. He, M. Tao and X. M. Yuan, Convergence rate analysis for the alternating direction method of multipliers with a

          substitution procedure for separable convex programming, Mathematics of Operations Research, 42 (2017) 662-691.

     7.  B. S. He, F. Ma and X. M. Yuan, An Agorithmic Framework of Generalized Primal-Dual Hybrid Gradient Methods for

           Saddle Point Problems, J. Math. Imaging Vis. 58 (2017) 279-293.

     8.  C. H. Chen, X. L. Fu, B.S. He and X. M. Yuan,  On the Iteration Complexity of Some Projection Methods for Monotone

           Linear Variational Inequalities, JOTA, 172(2017) 914-928.

     9. B. S. He, F. Ma and X. M. Yuan, Convergence study on the symmetric version of ADMM with larger step sizes, SIAM. J.

            Imaging Science  9 (2016) 1467-1501.

     10. C.H. Chen, B.S. He, Y.Y. Ye and X. M. Yuan,  The direct extension of ADMM for multi-block convex minimization

         problems is not necessary convergent, Mathematical Programming, 155 (2016) 57-79.

     11. B.S. He, H.K. Xu and X.M. Yuan, On the Proximal Jacobian Decomposition of ALM for Multiple-Block Separable

          Convex Minimization Problems and its Relationship to ADMM, J. Sci. Comput. 66 (2016) 1204-1217.

     12.  B.S. He and X.M. Yuan, Block-wise Alternating Direction Method of Multipliers for Multiple-block Convex Programming

          and Beyond, SMAI J.  Computational Mathematics 1 (2015) 145-174.       

     13. B.S. He, L.S. Hou, and X.M. Yuan, On Full Jacobian Decomposition of the Augmented Lagrangian Method for Separable

          Convex Programming, SIAM J. Optim., 25 (2015) 2274–2312.

      14. B.S. He and X. M. Yuan, On the convergence rate of Douglas-Rachford operator splitting method, Mathematical

         Programming, 153 (2015) 715-722.

     15. E.X. Fang, B.S. He, H. Liu and X. M. Yuan, Generalized alternating direction method of multipliers: new theoretical

           insights and applications, Mathematical Programming Computation, 7 (2015) 149-187.

     16. B.S. He and X.M. Yuan, On non-ergodic convergence rate of Douglas-Rachford alternating directions method of multipliers,

          Numerische Mathematik, 130 (2015) 567-577.

     17. B.S. He, M. Tao and X.M. Yuan, A splitting method for separable convex programming, IMA J. Numerical  Analysis,

          31(2015), 394-426.

     18. B. S. He, PPA-like contraction methods for convex optimization: a framework using variational inequality approach, J.

           Oper. Res. Soc. China 3(2015), 391-420.

     19. G.Y. Gu, B.S. He and  J.F. Yang, Inexact Alternating-Direction-Based Contraction Methods for Separable Linearly

          Constrained Convex Optimization,JOTA 163 (2014) 105-129.

     20. B. S. He, Y. F. You and X. M. Yuan, On the Convergence of Primal-Dual Hybrid Gradient Algorithm, SIAM. J. Imaging

            Science  7 (2014), 2526-2537.

     21.  B.S. He, H. Liu, Z.R. Wang and X. M. Yuan, A strictly Peaceman-Rachford splitting method for convex programming,

             SIAM J. Optim. 24 (2014),1011-1040.

     22.  G.Y. Gu, B.S. He and X.M. Yuan,  Customized proximal point algorithms  for linearly constrained convex minimization

            and saddle-point problems: a unified approach,  Comput. Optim. Appl., 59(2014), 135-161.

     23. Y. F. You, X.L. Fu and B.S. He, Lagrangian-PPA based contraction methods for linearly constrained convex optimization,

            Pac. J. Optim. (2014) 199-213.

     24. X.J. Cai, G.Y. Gu and B.S. He,  On the O(1/t) convergence rate of the projection and contraction methods for

           variational inequalities with Lipschitz continuous monotone operators,  Comput. Optim. Appl., 57(2014), 339-363.

     25. B.S. He, X.M. Yuan and W.X. Zhang, A customized proximal point algorithm for convex minimization with linear

            constraints,  Comput. Optim. Appl., 56(2013), 559-572.

     26. B.S. He and X.M. Yuan, Forward-backward-based descent methods for composite variational inequalities, Optimization

           Methods Softw. 28 (2013), 706-724.

     27. B.S. He, M. Tao, M.H. Xu and X.M. Yuan, An alternating direction-based contraction method for linearly constrained

           separable convex programming problems, Optimization, 62 (2013), 573-596.

     28. X.J. Cai, G.Y. Gu, B.S. He and X.M. Yuan, A proximal point algorithms revisit on the alternating direction method

            of multipliers, Science China Mathematics, 56 (2013), 2179-2186.

     29.  B.S. He, M. Tao and X.M. Yuan, Alternating Direction Method with Gaussian Back Substitution for Separable

            Convex Programming,  SIAM J. Optim. 22(2012), 313-340.
     30. B.S. He and X.M. Yuan, On the $O(1/n)$ Convergence Rate of the Douglas-Rachford
Alternating Direction

           Method,SIAM J. Numer. Anal. 50(2012), 700-709.

     31. B.S. He and X.M.Yuan, Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction

           perspective. SIAM J. Imaging Science. 5(2012), 119-149.

     32. C.H. Chen, B.S. He and X.M. Yuan, Matrix completion via alternating direction methods. IMA Journal of Numerical

           Analysis. 32(2012), 227-245.

     33. B.S. He, L.Z. Liao and X. Wang, Proximal-like contraction methods for monotone variational inequalitiesin a unified

           framework I: Effective quadruplet and primary methods, Comput. Optim. Appl., 51(2012), 649-679.

     34. B.S. He, L.Z. Liao, and X. Wang, Proximal-like contraction methods for monotone variational inequalities in a unified

           framework II: General methods and numerical experiments, Comput. Optim. Appl., 51(2012),  681-708.

     35. B.S. He, M.H. Xu, and X.M. Yuan, Solving large-scale least squares semidefinite programming by alternating direction

           methods. SIAM J. Matrix Anal. Appl. 32(2011), 136-152.

     36. B.S. He, W. Xu, H. Yang, and X.M. Yuan, Solving over-production and supply-guarantee problems in economic equilibria.

           Netw. Spat. Econ. 11(2011), 127-138.

     37. M. Tao, B.S. He, and X.M. Yuan, Solving a class of matrix minimization problems by linear variational inequality approaches.

           Linear Alge. Appl. 434(2011), 2343-2352.

     38. B.S. He, Z. Peng, and X.F. Wang, Proximal alternating direction-based contraction methods for separable linearly constrained

           convex optimization. F. M. C. (6)2011, 79-114.

     39. X. Wang, B.S. He, and L.Z. Liao,  Steplengths in the extragradient type methods. J. of Comput. Appl. Math.

           233 (2010), 2925-2939.

     40. B.S. He, X.Z. He, and Henry X. Liu, Solving a class of constrained ‘black-box’ inverse variational inequalities.

           European J. Oper. Res. 204 (2010), 391-401.

     41. X.L. Fu, and B.S. He, Self-adaptive projection-based prediction correction method for constrained variational inequalities.

          Front. Math. China. 5 (2010), no. 1, 3-21.

     42. H. Yang, W. Xu, B.S. He, and Q. Meng, Road pricing for congestion control with unknown demand and cost functions.

            Trans. Res. Part C. 18 (2010), 157-175.     

      

        Published papers from 2001 to 2009

 

        Published papers before 2000

  

                                                                                                                                                                                                                   Last Update: Sept. 30, 2019



Department of Mathematics, Nanjing University