学术报告一

讲座题目:交通科学中的一些数学问题

报告人：韩德仁 教授 北京航空航天大学

报告时间：2020年10月31日(星期六)上午9:00—9:45

报告地点：腾讯会议( ID:498 429 440)

摘要：The difficulty in implementation of marginal cost based toll collection is the absence of explicit expression of the demand function. In such circumstances, trial-and-error is usually among the best strategies. We first formulate this problem as a variational inequality problem with partial unknown mappings and then give an efficient implementation scheme. The global convergence of the method is proved and some numerical results are reported to illustrate its performance.

报告人简介：韩德仁，杰青、教授、博士生导师、北京航空航天大学数学科学学院经理。2002年获南京大学计算数学博士学位。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运筹学奖，江苏省科技进步二等奖等奖项。 主持多项国家科学基金项目，入选江苏省333高层次人才培养工程。担任中国运筹学会理事、数学规划分会常务理事；《Journal of Global Optimization》、《计算数学》、《Journal of the Operations Research Society of China》编委。

学术报告二

讲座题目:Alternating direction methods of multipliers for a generalized multi-facility Weber problem under gauge

报告人：蒋建林教授 南京航空航天大学

报告时间：2020年10月31日(星期六)上午9:50—10:35

报告地点：腾讯会议( ID:498 429 440)

摘要：A generalized multi-facility Weber problem (GMFWP), where the gauge is used to measure distances and some locational constraints are imposed to new facilities, is considered in this talk. This problem has many important applications in real situations, either itself or as subproblems. In order to solve the GMFWP efficiently, we reformulate it as a separable minimization problem and then several alternating direction methods of multipliers (ADMMs) are contributed to solving the separable problem. Specifically, for the problem with the locational constraint being $\Re^2$, a globally convergent ADMM method for two-block problem are presented; for the problem with locational constraint being a general convex set, an ADMM method for multi-block problem, which is fast but has no convergence guarantee, is adopted. One of main contribution of this paper is to propose a new linearized ADMM which is accelerated by an over-relaxation strategy for general multi-block problem and its global convergence is proved under mild assumption. We then apply it to solve the GMFWP. Some satisfactory numerical results for numerous GMFWPs are reported, which verify the efficiency of proposed ADMM methods.

报告人简介：蒋建林，教授，博士生导师，南京航空航天大学数学系主任，湖北省“楚天学者”特聘教授。曾担任国家自然科学基金委员会项目主任。2000年南京大学数学系计算数学专业获理学学士学位，2005年南京大学数学系计算数学专业获理学博士学位。研究方向为数值最优化、设施选址模型的研究与应用。在国内外正式刊物上发表学术论文40余篇。报告人与国内外学者合作密切，多次到新加坡、香港等地高校进行访问与交流。主持国家自然科学基金项目6项；参与国家自然科学基金项目3项。2014年获江苏省 “青蓝工程”培养对象。

学术报告三

讲座题目:Some inertial alternating proximal(-like) gradient methods for a class of nonconvex optimization problems

报告人：蔡邢菊 副教授(南京师范大学)

报告时间：2020年10月31日(星期六)上午10:40—11:25

报告地点：腾讯会议( ID:498 429 440)

摘要：We study a broad class of nonconvex nonsmooth minimization problems, whose objective function is the sum of a function of the entire variables and two nonconvex functions of each variable. For the different cases, we linearized different fart of the objective function, adopting inertial strategy to accelerate the convergence. We also propose an inertial alternating proximal-like gradient descent algorithm for the problem with abstract constraint sets whose geometry can be captured by using the domain of kernel generating distances. This algorithm can circumvents the restrictive assumption of global Lipschitz continuity of gradient. We prove that each bounded sequence generated by these algorithms globally converge to a critical point of the problem under the assumption that the underlying functions satisfy the Kurdyka-Łojasiewicz property.

报告人简介：蔡邢菊，南京师范大学副教授，硕导。主持国家面上基金、青年基金各一项，江苏省青年基金一项，国家博后特别资助一项。研究兴趣：最优化理论与算法，数值优化，交通管理中的优化，变分不等式。

学术报告四

讲座题目:Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion

报告人：何洪津 副教授(杭州电子科技大学)

报告时间：2020年10月31日(星期六)上午11:25—12:10

报告地点：腾讯会议( ID:498 429 440)

摘要：Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due to the multidimensional nature of high-order tensors, the matrix approaches, e.g., matrix factorization and direct matricization of tensors, are often not ideal for tensor completion and recovery. Exploiting the potential periodicity and inherent correlation properties appeared in real-world tensor data, in this talk, we shall incorporate the low-rank and sparse regularization technique to enhance Tucker decomposition for tensor completion. A series of computational experiments on real-world datasets, including internet traffic data, color images, and face recognition, show that our model performs better than many existing state-of-the-art matrix and tensor approaches in terms of achieving higher recovery accuracy. (Joint work with C. Pan, C. Ling, and L.Q. Qi).

报告人简介：何洪津，男，副教授，硕士生导师，2012年6月博士毕业于南京师范大学计算数学专业。主要研究方向为数值优化及其在图像处理、统计学习、机器学习等领域中的应用。研究成果发表在Numerische Mathematik, Inverse Problems, Journal of Scientific Computing 等国际权威期刊。主持国家自然科学面上基金等省部级以上项目4项，参与项目多项。2017年10月入选浙江省高校中青年学科带头