Professor Bingsheng He


















International Centre of Management Science and Engineering, Nanjing University

Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China

Phone: +86-25-83593362



Current Research Areas:

Mathematical Programming,  Numerical Optimization,  Variational Inequalities



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

Thesis Advisor: Professor Dr. Josef Stoer

BSc: Computational Mathematics, Nanjing University, 1981



1997~Now   Professor, Nanjing University

1992~1997  Associate Professor, 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 — 一路走来

     2. 凸优化的分裂收缩算法 — 变分不等式为工具的统一框架










                     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.)





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

          Online published in Numerische Mathematik

      2. 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, Online published in Mathematical Programming.

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

       Mathematical Programming.

      4. B.S. He, M. Tao and X.M. Yuan, A splitting method for separable convex programming, Online published in IMA Journal

          of Numerical  Analysis.

      5. 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.

      6.  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.

      7.  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.

      8. 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.

      9. 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.

      10. 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.

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

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

      12. 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.

      13. 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.

     14.  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.
     15. 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.

     16. 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.

     17. 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.

     18. 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.

     19. 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.

     20. 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.

     21. 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.

     22. 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.

     23. 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.

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

           233 (2010), 2925-2939.

     25. 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.

     26. 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.

     27. 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.     

     28. B.S. He, X. Wang, and J.F. Yang, A comparison of different contraction methods for monotone variational inequalities.

            J. Comput. Math. 27 (2009), no. 4, 459-473.    

     29. B.S. He, X.L. Fu, and Z.K. Jiang, Proximal-point algorithm using a linear proximal term. J. Optim. Theory Appl.

            141 (2009), no. 2, 299-319.
      30. B.S. He, X.Z. He, Henry X. Liu, and T. Wu, Self-adaptive projection method for co-coercive variational inequalities.

            European J. Oper. Res. 196 (2009), no. 1, 43-48.
      31. B.S. He, Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities.

            Comput. Optim. Appl. 42 (2009), no. 2, 195-212.
      32. B.S. He, M. Li, and L.Z. Liao, An improved contraction method for structured monotone variational inequalities.

            Optimization 57 (2008), no. 5, 643-653.
      33. B.S. He, and M.H. Xu, A general framework of contraction methods for monotone variational inequalities.

            Pac. J. Optim. 4 (2008), no. 2, 195-212.


        Published papers from 2001 to 2007


        Published papers before 2000


                                                                                                                                                                                                                   Last Update: December. 15, 2014 

Department of Mathematics, Nanjing University