一、报告题目：求解线性方程组和不等式组的随机算法
报告人简介：
韩德仁，教授，博士生导师，现任北京航空航天大学数学科学学院院长。从事大规模优化问题、变分不等式问题的数值方法的研究工作，以及优化和变分不等式问题在交通规划、磁共振成像中的应用，发表多篇学术论文。曾获中国运筹学会青年科技奖，江苏省科学技术奖等奖项；主持国家自然科学基金杰出青年基金等多项项目。担任中国运筹学会常务理事、算法软件与应用分会理事长；《数值计算与计算机应用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》编委。
报告内容简介：
本报告介绍求解相容和不相容线性方程组和不等式组问题的随机算法的几个新进展，包括多集合Douglas-Rachford分裂算法（r-sets-DR (RrDR)）等。
二、报告题目：模型驱动与数据驱动的优化反演问题及智能计算
报告人简介：
王彦飞，研究员，从事反问题理论及正则化方法、反问题的数学优化算法、计算及勘探地球物理、地学大数据与人工智能分析研究工作。主持国家重点研发计划、基金重大计划项目等多项，发表论文150余篇，出版学术论著6部，授权发明专利30余项。任中国科学院油气资源研究重点实验室主任、地球科学大数据与人工智能中心主任、大数据分析与人工智能地球物理学科组组长。入选多个国家高层次人才计划。任中国运筹学会及数学智能分会常务理事、CSIAM反问题与成像专委会副主任。获中国青年科技奖、国务院政府特殊津贴专家等多项荣誉。
报告内容简介：
In the field of geophysics, big data, AI, and inverse problems involve cross-disciplinary integration of computer science, mathematics, statistics, and geophysics. This approach enables the development of accurate subsurface property models by analyzing vast amounts of geophysical data. Traditionally, various geophysical methods were used to study geological anomalies, but the use of big data and AI has shown potential to enhance this process. This talk will introduce both model-driven and data-driven inverse problems and explain how optimizing algorithms are used to solve for physical properties of the earth’s subsurface from geophysical data collected at the surface.
三、报告题目：Regularized splitting method for three operators inclusion problems of “two maximal monotone + one cocoercive” and its applications
报告人简介：
蔡邢菊，南京师范大学教授，博士生导师。主要从事最优化理论与算法、变分不等式、数值优化方向研究工作。主持多项国家基金，获江苏省科技进步奖一等奖一项，发表SCI论文50余篇。担任中国运筹学会副秘书长、算法软件与应用分会秘书长、数学规划分会常务理事，江苏省运筹学会理事长。
报告内容简介：
Thisstudyconsiders finding a zero point of A + B + C, where A and C are maximal monotone and B is ξ-cocoercive. The three-operator splitting method (TSM), proposed by Davis and Yin, is a popular algorithm for solving this problem. Observing that the x-sequence and the y-sequence in TSM have the same accumulation point and B’s information is only utilized in the second subproblem, this work proposes a new splitting method named the regularized splitting method (RSM), where “x = y” is introduced as a penalty term and the forward step is also employed in the first subproblem. The penalty term can balance the differences between the two subproblems and the additional forward step enables utilizing B’s information in both subproblems simultaneously. We establish the convergence of the proposed method and demonstrate its sublinear convergence rate concerning the fixed-point residuals, assuming mild conditions in an infinite dimensional Hilbert space. This approach not only generalizes the Douglas-Rachford splitting method and the TSM, but also, to our knowledge, uniquely correlates with the symmetric alternating direction method of multipliers–a correspondence that is absent in current maximal monotone operator splitting algorithms. As an application, we use RSM to solve zero point problems involving multiple operators. By introducing a new space reconstruction method, we transform the problem of multiple operators into a problem of three operators and derive a distributed version of the RSM. We validate our method’s efficiency through applications to mean-variance optimization, inverse problems in imaging, and the softmargin support vector machine problem with nonsmooth hinge loss functions, showcasing its superior performance compared to existing algorithms in the literature.
四、报告题目：Simulated annealing-based nonmonotone conjugate gradient method for unconstrained optimization with applications
报告人简介：
彭拯，湘潭大学数学与计算科学学院教授，博士生导师。主要从事数学优化理论、算法及其应用研究，当前研究兴趣在于流形优化与流形学习，以及超大规模集成电路物理设计、下一代通信网络、新能源电力系统等理论与实际应用中的大规模非凸非光滑优化问题的求解算法，尤其关注随机优化算法与非单调优化算法相关研究。主持国家重要科研项目6项，省部级项目5项。当前兼任中国运筹学会理事、湖南省运筹学会副理事长，中国运筹学会算法软件及其应用分会常务理事和数学规划分会理事。
报告内容简介：
Line search methods typically require a large number of iterations to find the suitable stepsize, resulting in slower convergence speed and higher computation cost. Combining with nonmonotone simulated annealing technique and Armijo line search, we propose a modified three-term conjugate gradient method to reduce the numbers of line search method used. For a given trial stepsize, we decide whether to accept it by simulated annealing rule; If not accepted, Armijo line search is then utilized. Under some mild conditions, the global convergence of the proposed method is established without the gradient Lipschitz continuous condition. Compared to some existing methods for unconstrained optimization problems, numerical experiments demonstrate that the proposed algorithm is promising for the testing problems.
五、报告题目：Adaptive stepsize for Douglas-Rachford splitting algorithm and ADMM
报告人简介：
徐玲玲，南京师范大学数学科学学院副教授，硕士生导师。主要从事最优化理论与算法方面的研究，主持国家自然科学基金青年基金一项，江苏省高校自然科学基金一项，目前主持国家自然科学基金面上基金一项，科学与工程计算国家重点实验室开放课题(重点)一项，参加国家重点研发计划一项，担任中国运筹学会宣传委员会副主任、江苏省运筹学会常务副秘书长等职。
报告内容简介：
The Douglas-Rachford (DR) splitting algorithm is a classical first-order splitting algorithm for solving maximal monotone inclusion problems. We propose an adaptive stepsize for DR splitting algorithm (ADR), which sets the step size based on local information of the objective function, and only requires two extra function evaluations per iteration. We prove the global convergence of ADR and the sublinear convergence rate of the objective function value in the ergodic sense. In addition, we apply ADR to solve the dual problem of the separable convex optimization problem with linear equality constraints and obtain an alternating direction method of multipliers with line search (ADMM-LS). By demonstrating the relationship between ADR and ADMM-LS, we prove the global convergence of ADMM-LS. Finally, we test three numerical experiments to compare the ADR and ADMM-LS with other algorithms. The numerical results verify the effectiveness and efficiency of ADR and ADMM-LS.
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理学院
2024年9月20日
