“数通古今，学贯中外”学术讲座第四十二期预告【戚厚铎副教授】

时　间: 2013年1月17日(周四)15:30-16:30

地　点:研究生楼106

报告人: Houduo Qi （戚厚铎），University of Southampton, UK

报告人简介:

戚厚铎, http://www.personal.soton.ac.uk/hdqi
　　现为英国南安普敦大学高级讲师，博士生导师。1990年毕业于北京大学统计学专业，1993年获曲阜师范大学硕士学位, 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。在国际顶级期刊SIAM on Optimization, Mathematical Programming 等杂志发表高水平研究论文十余篇。

Title: Computing the Nearest Euclidean Distance Matrix with Low Embedding Dimensions

Abstract: Euclidean distance embedding appears in many high-profile applications including wireless sensor network localization, where not all pairwise distances among sensors are known or accurate. The classical Multi-Dimensional Scaling (cMDS) generally works well when the partial or contaminated Euclidean Distance Matrix (EDM) is close to the true EDM, but otherwise performs poorly. A natural step preceding cMDS would be to calculate the nearest EDM to the known matrix. A crucial condition on the desired nearest EDM is for it to have a low embedding dimension and this makes the problem nonconvex.
　　There exists a large body of publications that deal with this problem. Some try to solve the problem directly and some are the type of convex relaxations of it. In this paper, we propose a numerical method that aims to solve this problem directly. Our method is strongly motivated by the majorized penalty method of Gao and Sun for low-rank positive semi-definite matrix optimization problems. The basic geometric object in our study is the set of EDMs having a low embedding dimension. We establish a {/em zero} duality gap result between the problem and its Lagrangian dual problem, which also motivates the majorization approach adopted. Numerical results show that the method works well for the Euclidean embedding of Network coordinate systems and for a class of large scale sensor network localization problems. This is a joint work with Dr Yuan Xiaoming of Hong Kong Baptist University.