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Professor Bingsheng He
Department of Mathematics, Nanjing University, Nanjing, 210093, China E-mail: hebma@nju.edu.cn
Current Research Areas: Mathematical Programming, Numerical Optimization, Variational Inequalities, Projection and contraction methods for VI, 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: 2015-2020 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
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. 古稀回首 4. 说说我的主要研究兴趣(续) --- 我们在ADMM类方法的主要工作 两页短文A-H的导读 A. 我的主要研究历程-从变分不等式的投影收缩算法到凸优化的分裂收缩算法 B. PC方法中的孪生方向和姊妹方法 C. 两页纸给出ADMM 收敛性证明 D. 凸优化问题相应的变分不等式以及为几类典型问题构造的邻近点算法 E. 统一框架下求解两个可分离块凸优化问题的 效率更高的ADMM算法 F. 统一框架下求解三个可分离块凸优化问题的算法-高斯回代和正则化方法 G. 古稀后的研究进展-I: 从好不容易凑出一个方法到并不费力构造一簇算法 H. 古稀后的研究进展-II：预测-校正的广义邻近点(Generalized PPA)算法 视上述A-H八篇为八个单元扩展成较为详细并加些例子说明的16篇两页短文-加上前言导读和参考文献的文本 《数学文化》2020 年/ 第 11 卷第 2 期刊登的我的自述: 四十年上下求索 一份珍贵的回忆材料 My Talks: 比较系统的知识建议阅读第3个报告. 也建议阅读最近的一些系列报告
For more systematic knowledge, it is recommended to read Talk 3, which is written in English.
23. 2024 年 春季在华师大_上海大学_复旦大学_南京应用数学中心_西工大_西交大_西电的报告 导读 报告
22. 2024 年2月在三亚“数学、图像科学与人工智能”研讨会的两个报告的内容摘要 报告I 报告II
21. 从PPA-ADMM到凸优化的广义PPA (2023年12 月6日应西电数学与统计学院邀请的90分钟的报告)
20. 2023 年11月在 曲阜师大两次（共计四小时）课程的PPT 两次课程的内容摘要 课程I 课程II
19. 2023 年10月在天元数学东北中心八次课程的汇总讲义 前言与目录 I II III IV V VI VII VIII
18. 2023年1月在华南师大《华人数学家论坛》的报告 — 凸优化分裂收缩算法统一框架的最新进展
17. 2022年11月在西电《最优化前沿论坛》的报告 — 从好不容易凑出一个算法到并不费劲构造一簇算法
16. 2022 年7月南理工《计算机》方向暑期班六讲摘要 和六讲 每讲的 PPT I II III IV V VI
15. 利用预测-校正统一框架构造凸优化的分裂收缩算法(由预测矩阵构造校正矩阵) (ArXiv: 2204.11522) 14. 2022 年元月南师大数科院系列报告B站视频辅助材料 A B C D E F G H I J K L 13. ADMM 类分裂收缩算法的一些最新进展 统一框架下Balanced-ALM 便于向多块推广的ADMM 12. 均困平衡的增广拉格朗日乘子法 — Balanced ALM (一类新的增广拉格朗日乘子法ArXiv: 2108.08554) 11. 一类便于向求解多块问题推广并能处理不等式约束问题的交替方向法 (ArXiv:2107.01897) 10. 瞎子爬山-步步为营—凸优化算法中的变分不等式和邻近点策 略(南京大学数学系本科生论坛上的报告) 9. 被S. Becker 誉为 Very Simple yet Powerful 的 Technique — 应用及新的进展 8. 线性化ALM 线性化ADMM 以及处理三个可分离块问题中缩小有关参数至3/4提高效率的方法 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 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 5. 我和乘子交替方向法(ADMM) 的20年 — 2017 年5月全国数学规划会议报告 综述版本 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 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) 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 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 注：报告 6(6:08:43), 7(36:53), 10(1:19:05) 的相关视频可在 Bilibili 搜索 "何炳生" 找到 My Foundations: 感谢各类基金的资助 细水长流 让我得以培养研究生 独立 开展数学研究 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
前言目录及各部分-2020 新版内容说明 适合打印的 2020 新版系列讲义
第一部分：单调变分不等式的求解方法
第2讲. 三个基本不等式和变分不等式的投影收缩算法
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8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. 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. 统一框架下交替方向法的收敛速率研究
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
Lectures of 'Contraction Methods for Convex Optimization and Monotone Variational Inequalities'
Working Papers (Some of recent research manuscripts are included.)
55. B.S. He, New progress in a unified framework of splitting and contraction methods for convex optimization--From struggling to put together a method to effortlessly constructing a family of algorithms (in Chinese). Numerical Mathematics - A Journal of Chinese Universities, 46 (2022), 1-22 54. B.S. He, F. Ma, S.J. Xu and X.M. Yuan, A rank-two relaxed parallel splitting version of the augmented Lagrangian method with step size in (0,2) for separable convex programming, Mathematics of Computation, 92(2023), 1633-1663. 53. B.S. He, S.J. Xu and X.M. Yuan, Extensions of ADMM for separable convex optimization problems with linear equality or inequality constraints, Handbook of Numerical Analysis, 24 (2023) 511-557. arXiv:2107.01897v2[math.OC]. 52. B.S. He, Using a unified framework to design the splitting and contraction methods for convex optimization (in Chinese). Numerical Mathematics - A Journal of Chinese Universities, 44 (2022), 1-35 Paper Download 51. B.S. He, F. Ma, S.J. Xu and X.M. Yuan, A generalized primal-dual algorithm with improved convergence condition for saddle point problems. SIAM J Imaging Sci., 15(3), 1157-1183 (2022) 50. B.S. He, S.J. Xu, X.M. Yuan, On Convergence of the Arrow–Hurwicz Method for Saddle Point Problems. J Math Imaging Vis 64, 662–671 (2022). 49. B.S. He and X.M. Yuan, On the optimal proximal parameter of an ADMM-like splitting method for separable convex programming. Mathematical methods in image processing and inverse problems, 139–163, Springer Proc. Math. Stat., 360. Springer, Singapore, 2021. 48. S.J. Xu and B.S. He, A parallel splitting ALM-based algorithm for separable convex programming, Comput. Optim. Appl. 80 (2021), 831–851. 47. B.S. He, Study on the Splitting Methods for Separable Convex Optimization in a Unified Algorithmic Framework, Analysis in Theory and Applications, 26 (2020) 262-282. 46. B.S. He, F. Ma and X.M. Yuan, Optimally linearizing the alternating direction method of multipliers for convex programming, Comput. Optim. Appl. 75 (2020), 361-388. 45. 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. 40 (2020)， 1188-1216. 44. B. S. He, M. 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. 43. B. S. He, My 20 years research on alternating directions method of multipliers. (Chinese) Oper. Res. Trans. 22 (2018), 1–31. DOI: 10.15960/j.cnki.issn.1007-6093.2018.01.001 42. 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. 41. B. S He, A uniform framework of contraction methods for convex optimization and monotone variational inequality. (Chinese) Scientia Sinica Mathematica 48 (2018) 255-272 40. 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. 39. 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. 38. 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. 37. 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. 36. 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. 35. 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. 34. B.S. He, Modified alternating directions method of multipliers for convex optimization with three separable functions. (in Chinese) Oper. Res. Trans. Vol.19 No.3 (2015), 57–70. DOI: 10.15960/j.cnki.issn.1007-6093.2015.03.008 33. 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. 32. 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. 31. B.S. He and X. M. Yuan, On the convergence rate of Douglas-Rachford operator splitting method, Mathematical Programming, 153 (2015) 715-722. 30. 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. 29. 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. 28. B.S. He, M. Tao and X.M. Yuan, A splitting method for separable convex programming, IMA J. Numerical Analysis, 31(2015), 394-426. 27. 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. 26. 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. 25. 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. 24. 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. 23. 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. 22. 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. 21. 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. 20. 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. 19. B.S. He and X.M. Yuan, Forward-backward-based descent methods for composite variational inequalities, Optimization Methods Softw. 28 (2013), 706-724. 18. 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. 17. 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. 16. B.S. He and Y. Shen, On the convergence rate of customized proximal point algorithm for convex optimization and saddle-point problem (in Chinese). Sci Sin Math, 2012, 42(5): 515–525, doi: 10.1360/012011-1049 15. B.S. He and X.M. Yuan, An accelerated inexact proximal point algorithm for convex minimization，JOTA 154 (2012), 536-548. 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. Method，SIAM J. Numer. Anal. 50(2012), 700-709. 12. 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. 11. 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. 10. 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. 9. 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. 8. 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. 7. 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. 6. 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. 5. 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. 4. X. Wang, B.S. He, and L.Z. Liao, Steplengths in the extragradient type methods. J. of Comput. Appl. Math. 233 (2010), 2925-2939. 3. 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. 2. 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. 1. 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
Last Update: May 5, 2024 |
