信息公告
数理学院数学学科系列学术报告(7月19日)
发布时间:2016-07-15 
报告题目: Correctness and Convergence of Belief Propagation for Multicommodity Min-Cost Flow
报告人:张晓岩(南京师范大学数科院)
时间:719(周二) 9:00-10:00
地点:数理楼2517.
摘要:Belief Propagation (BP), a distributed, message-passing algorithm, has been widely used in modern coding theory, artificial intelligence and combinatorial optimization problems in graphical models such as Bayesian networks and Markov random fields due to its simple and iterative message-passing nature [Science(20022003)] . It is well known that if the graphical models (GMs) are cycle free, the BP algorithms converge to the correct solutions. However, the correctness and convergence of BP are still open problems for GMs with arbitrary underlying graph.  
In this talk, we investigate the multicommodity min-cost flow problem (MMCF) which is a generalization of the multicommodity maximum total flow problem (MMTF) and the minimum cost network flow problem (MCF). For MMTF, the solution provides dedicated bandwidth r between each source-sink pair, which is one of the two different models of k-pairs communication problem while the other is the network information flow model (network coding). For MCF, it is well known that it has been one of the fundamental problem in the development of polynomial time algorithms for optimization problems. During the past decades, a variety of efficient algorithms for MCF have been proposed.
Despite BP has a great success in many application fields, the rigorous analysis about the correctness and convergence of BP are known in only a few cases. Motivated by the reason to understand the structure of more general optimization problems precisely which are achievable by BP, we prove that BP converges to the optimal solution of MMCF within O(n) iterations, provided that it has the unique optimal solution. We further provide the asynchronous updating schemes of belief propagation for solving MMCF.
报告人简介:张晓岩, 男,南京师范大学数学科学学院及数学研究所教授,南京师范大学“百名青年领军人才”,“青蓝工程”优秀中青年学术带头人,获得南开大学应用数学博士学位及荷兰Twente大学理论计算机科学博士学位,主要从事算法图论与结构图论、组合优化及理论计算机科学的研究工作,近年来在图与超图的划分、图上细胞自动机问题、路覆盖、有向Hamilton圈及网络信息流等问题的组合结构及随机算法方面取得了一系列理论成果,已在国内外有重要影响的学术期刊SIAM J. COMPUTING、SIAM J. DISCRETE MATH、J. GTAPH THEORY、THEO COMPUT SCI、ACM/SPRINGER MOBILE NETW APPL、SCIENCE CHINA MATH等发表或已接收发表学术论文四十余篇。
报告题目: 道路收费问题的数值方法及效率分析
报告人:韩德仁(南京师范大学数科院)
时间:719(周二) 15:00-16:00
地点:数理楼2517.
摘要:随着经济的发展,城市交通拥堵问题是一个日益突出的问题。收费是缓解交通拥堵的一个有效手段。设计收费方案的难点之一是需求函数未知(不确定)。本报告首先回顾拥堵收费中的优化(变分不等式)模型,然后给出求解这些模型的数值方法,并对收费的效果给出分析。
报告人简介:韩德仁教授1993考入南京大学数学系,2002获得理学博士学位。先后于微软亚洲研究院、新加坡—MIT学术联盟(SMA)、香港理工大学、香港科技大学、香港城市大学、香港浸会大学等高校或研究机构从事博士后或访问工作。现为江苏省333高层次人才、南京师范大学数学科学学院教授。曾获得中国运筹学会青年运筹学奖二等奖,江苏省科技进步二等奖等奖项。已在Mathematical Programming, SIAM Journal on Numerical Analysis, Mathematics of Computation, Numerische Mathematik等期刊发表SCI论文70余篇。目前担任中国运筹学数学规划分会常务理事、《计算数学》编委。他的研究兴趣涉及变分不等式和互补问题、交通规划以及图像处理等领域。
报告题目: Uncertain Linear Optimization, Asset Inequality and Vulnerability of the Financial Network
报告人:Jiming Peng (Department of Industrial Engineering, University of Houston)
时间:719(周二) 16:00-17:00
地点:数理楼2517.
摘要: Since the financial crisis in 2007-2008,systemic risk in a financial network has become a major concern in financial engineering and economics.In this talk, we study the vulnerability of a financial network based onthe linear optimization model introduced by Eisenberg and Noe (2001), where the right hand side of the constraints is subject to market shockand only partial information regarding the liability matrix is revealed.We conduct a new sensitivity analysis to characterize the conditionsunder which a single bank is solvent, default or bankrupted, and estimate the probability that some financial institute in the network willbe bankrupted under mild assumptions on the market shock and the network structure.    We also show that the asset inequalities among the banks have a negative impact on the efficiency and stability of the network, and demonstrate that the bailout of big banks may not stop the domino effect regarding the bankruptcy in a network with a ring structure dominated by a monopoly,which is also the most vulnerable network.
报告人简介:Jiming Peng is an associate professor in the department of industrial engineering, University of Houston. Prior to this, he had worked in McMaster University in Canada and University of Illinois at Urbana-Champaign. His recent research interest lies mainly in optimization modeling, algorithm design with applications to healthcare, big data and finance. He has published a research monograph by Princeton University Press and about sixty papers in major optimization journals and highly ranked CS/IEEE conference proceedings. His research has been recognized by numerous awards from different academic communities and supported by various funding agencies in Canada and USA.
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