Assoc. Prof. Xiaomei Qu, Southwest University for Nationalities, China
Dr. Xiaomei Qu is an Associate Professor at the College of Computer Science and Technology, Southwest Minzu University, Chengdu, China. After receiving her PhD in Probability and Statistics at the College of mathematics, Sichuan University in 2010, Dr. Qu served as a Research Fellow at School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, from 2011 to 2013. Her research interests include mathematical programing, stochastic analysis, correlation modeling and analysis, optimization algorithms and their applications in information fusion, source localization and target tracking in wireless sensor networks. She has published over 30 academic papers in distinguished international journals and conferences including IEEE transactions on Signal Processing, Applied Mathematics Letters, Signal Processing, IEEE signal processing letters, etc. Her works in Geolocation and Tracking with Networked Multi-Sensor Platforms received the Best Paper Awards in Chinese Conference on information fusion in 2013 and 2017. She was elected a Committee Member in Information Fusion Branch of Chinese Aviation Association in 2015.
Title: Fast Algorithms for Solving Quadratic Constrained Quadratic Problems and Their Applications
Abstract: In the past decades, QCQP has become an important class of optimization problems that arise in various science and engineering fields. For a general non-convex QCQP problem, even establishing (in)feasibility is NP-Hard. A popular polynomial-time approximation strategy for obtaining a sub-optimal solution is the semidefinite relaxation (SDR) strategy. We found that QCQP with only one quadratic constraint possesses hidden convexity and exact solution could be obtained in polynomial time. For the QCQP with more than one quadratic constraint, we proposed an iterative approximate method which performs a linearization procedure on the quadratic constraints that can be analytically solved. Theoretical analysis reveals that the proposed method converges to the global optimal solution if it converges. Our methods are applied in passive source localization problems, and the localization accuracy is significantly improved over the previous methods with much less computation time requirement.