Professor Bingsheng He

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Department of Mathematics, SUSTC

(South University of Science and Technology of China),

Shenzhen, 51800, China  

Phone: +86-755-88018721   Email: hebs@sustc.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

 

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, South University of Science and Technology of China

    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

 



   

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

 


 

     Supervised Students

 


 

     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


 

     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


   

     凸优化和单调变分不等式的收缩算法

                                          

                                           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.    单调变分不等式收缩算法的统一框架

 

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

 

                     第4讲.    为线性约束凸优化问题定制的PPA算法及其应用

 

                     第5讲.    线性约束凸优化问题基于松弛PPA的收缩算法

 

                     第6讲.    线性约束凸优化扩展问题的PPA和松弛PPA收缩算法

 

                     第7讲.    基于增广Lagrange乘子法的PPA收缩算法

 

             第三部分:基于投影梯度的收缩算法

 

                    第8讲.     基于梯度投影的凸优化收缩算法和下降算法

 

                    第9讲.     线性约束凸优化基于对偶上升的自适应方法

 

                    第10讲.   线性约束单调变分不等式的自适应投影收缩算法

 

             第四部分: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

 

                    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

 

                    第14讲.   定制PPA意义的线性化交替方向法

 

             第五部分:多个可分离算子凸优化问题带简单校正的分裂方法

 

                    第15 讲.   三个可分离算子凸优化的平行分裂增广Lagrange乘子法

 

                    第16 讲.   三个可分离算子凸优化的略有改动的交替分向法


                    第17 讲.   多个可分离算子凸优化带回代的交替方向收缩算法


                    第18 讲.   多个可分离算子凸优化带回代的线性化交替方向法

 

             第六部分:计算复杂性分析

 

                    第19 讲.  Lipschitz-连续的单调变分不等式投影收缩算法的收敛速率

 

                    第20 讲.  交替方向法的计算复杂性和收敛速率

 


 

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

 


 

     Publications:      

      

      1. 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.

      2. 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.

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

         Programming, 153 (2015) 715-722.

      4. 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.

      5  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.

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

          31(2015), 394-426.

      7. 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.

      8. 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.

      9.  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.

      10.  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.

      11. 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.

      12. 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.

      13. 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.

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

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

      15. 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.

      16. 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.

     17.  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.
     18. 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.

     19. 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.

     20. 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.

     21. 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.

     22. 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.

     23. 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.

     24. B.S. He, W. Xu, Y. Hai, and X.M. Yuan, Solving over-production and supply-guarantee problems in economic equilibria.

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

     25. 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.

     26. 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.

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

           233 (2010), 2925-2939.

     28. 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.

     29. 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.

     30. 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: March. 25, 2015 



Department of Mathematics, Nanjing University