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甬江数学讲坛198讲(2021年第57讲)
2021-11-09 10:04     (点击:)

报告题目:A Facial Reduction Approach to the Single Source Localization Problem

人:李庆娜(北京理工大学教授)

报告时间:20211112 上午1000开始

报告地点:腾讯会议 493 506 209

报告摘要:The single source localization problem (SSLP) appears in several fields such as signal processing and global positioning systems. The optimization problem of SSLP is nonconvex and it is difficult to find the global optimal solution. It can be reformulated as a rank constrained Euclidean distance matrix (EDM) completion problem with a number of equality constraints. In this paper, we propose a facial reduction approach to solve such EDM completion problem. For the constraints of fixed distances between sensors, we reduce them to a face of the EDM cone and derive the closed formulation of the face. We prove constraint nondegeneracy for each feasible point of the resulting EDM optimization problem without rank constraint. To tackle the nonconvex rank constraint, we apply the majorized penalty approach developed by Zhou et al. (IEEE Trans Signal Process 66(3):43314346, 2018). Numerical results verify the fast speed of the proposed approach while giving comparable quality of solutions as other methods.

报告人简介:李庆娜,北京理工大学数学与统计学院教授,博士生导师。湖南大学本科、博士,中科院数学与系统科学研究院博士后. .曾访问英国南安普顿大学,新加坡国立大学、香港中文大学等。主持国家自然科学基金青年、面上项目等. 中国运筹学会数学优化分会青年理事,北京运筹学会理事。著有专著《多维标度方法》,教材《最优化方法》、《凸分析讲义》等三部。指导多名本科生创新竞赛并发表学术论文。获2020年北京市高校优秀毕业设计指导教师荣誉称号。主要研究最优化理论与算法及应用。

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