信息公告
数理学院数学学科系列学术报告(9月27日)
发布时间:2016-09-23 

报告题目: Matrix optimization model and algorithms for nonmetric-MDS

报告人:李庆娜(北京理工大学)

时间:927(周二)  14:30-15:30

地点:数理楼3304.

摘要: When the coordinates of a set of points are known, the pairwise Euclidean distances among the points can be easily computed. Conversely, if the Euclidean distance matrix is given, a set of coordinates for those points can be computed through the well known classical Multi-Dimensional Scaling (MDS). In this talk, we consider the case where some of the distances are far from being accurate (containing large noises or even missing). In such a situation, the order of the known distances (i.e., some distances are larger than others) is valuable information that often yields far more accurate construction of the points than just using the magnitude of the known distances. The methods making use of the order information is collectively known as non-metric MDS. A challenging computational issue among all existing nonmetric MDS methods is that there are often a large number of ordinal constraints. In this paper, we cast this problem as a matrix optimization problem with ordinal constraints. We then adapt an existing smoothing Newton method to our matrix problem. Extensive numerical results demonstrate the efficiency of the algorithm, which can potentially handle a very large number of ordinal constraints.

This is a joint work with Houduo Qi from University of Southampton.

报告人简介:李庆娜,北京理工大学副教授,2010年毕业于湖南大学,2010-2012年在中科院数学与系统科学研究院做博士后, 20126月加入北京理工大学。主要从事最优化理论与算法的研究,曾主持国家自然科学基金青年项目,今年刚获批国家自然科学基金面上项目。

报告题目: Locally Linear Embedding for Metric Dissimilarities

报告人:戚厚铎(南安普顿大学)

时间:927(周二)  15:30-16:30

地点:数理楼3304.

摘要: Locally linear embedding (widely known as LLE) is one of the top dimensionality reduction methods by Roweis and Saul (Science, 2000). LLE has since been widely used in many fields, mainly representing high dimensional data in a lower dimensional space, where data can be more efficiently investigated. Its input can take one of two forms: the coordinate matrix data or the pairwise Euclidean distance matrix of data. This talk aims to address one particular issue where the input data has noises or even has missing values. We refer to this type of input data as metric dissimilarities. The purpose of this talk is to report a new variant of LLE for metric dissimilarities. The key step is to replace the dissimilarities by its nearest Euclidean distance matrix, but at a local level. This step is achieved by a fast semismooth Newton-CG method. We prove the new variant will reduce to the original LLE when the input is taken to be one of the original forms. We illustrate its efficiency through a number of standard dimensionality reduction problems.

报告人简介:戚厚铎,英国南安普顿大学高级讲师,博士生导师。1990年毕业于北京大学统计学专业,1996年中国科学研究院数学与系统科学研究院应用数学研究所博士毕业。曾在香港理工大学、新南威尔士大学等做博士后研究,获澳大利亚研究委员会(ARC)资助,以及ARC和享有全球盛誉的Queen Elizabeth II Fellowship奖励。现为亚太运筹学杂志(APJOR)副主编。研究方向有:约束优化、矩阵优化、变分不等式、数值分析等。论文发表在SIAM J. Optimization, Mathematical Programming 等期刊。

报告题目: 订单排序模型及理论

报告人:李荣珩(湖南师范大学)

时间:927(周二)  16:30-17:30

地点:数理楼3304.

摘要: 经典排序问题考虑的参数是固定的,如加工时间,交货期,就绪时间和权等都是给定的常数,并且所有信息数据都归总到唯一决策者,由这个唯一的决策者进行总优化。也就是所谓的计划经济。订单排序问题是工件客户方向机器代理方以订单方式提出加工请求,机器代理方根据订单参数确定加工策略。机器方与客户方各有不同的利益目标,如何使各方达到最大利益,这是所谓的市场经济。我们将简要介绍一些订单排序模型与理论成果。

报告人简介:李荣珩,湖南师范大学数学与计算机科学学院教授,主要从事组合优化等方向的研究,从1989年开始从事离散问题的近似算法的分析与计算复杂性的证明与分类,曾在新加坡国立大学访问研究四年。设计了一个平行机问题的有效算法,改进了FFD算法的近似性估计,证明了两个组合问题的SNP-Hard性及两个选址问题的NP-完全性。提出了订单排序模型,并给出了一个近似比不超过2.9392的启发式算法,美国《Math. Rev. 》的评论认为该排序模型将会引起所有排序研究工作者的兴趣。结果主要发表在SIAM J. ComputingComputing等刊物。

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