SPS Webinar: Nonconvex Complex Quadratic Programs: New Semidefinite Relaxations, Global Algorithms, and Signal Processing Applications

Date: 14 September 2023
Time: 7:30 AM ET (New York Time)
Speaker(s): Dr. Cheng Lu, Dr. Ya-Feng Liu, Dr. Jing Zhou


We consider a class of nonconvex complex quadratic programming problems, which find a broad spectrum of signal processing applications. By using the polar coordinate representations of the complex variables, we first derive a new enhanced semidefinite relaxation for the problem. Based on the newly derived semidefinite relaxation, we further propose an efficient branch-and-bound algorithm for solving the problem. Key features of our proposed algorithm are: (1) it is guaranteed to find the global solution of the problem (within any given error tolerance); (2) it is computationally efficient because it carefully utilizes the special structure of the problem. We apply our proposed algorithm to solve a series of signal processing problems. Simulation results show that our proposed enhanced semidefinite relaxation is generally much tighter than the conventional semidefinite relaxation, and our proposed global algorithm can efficiently solve these problems.


Cheng LuCheng Lu received the B.Sc and Ph.D. degrees in mathematics from the Department of Mathematical Sciences, Tsinghua University, Beijing, China, in 2006 and 2011, respectively.

He is currently an Assistant Professor at North China Electric Power University since 2016. He worked at Media Lab of Huawei Central Research Institute from 2011-2013 and was a Postdoctoral Associate in the Department of Electronic Engineering, Tsinghua University from 2013-2016.

Dr. Lu received the Best Paper Award from Journal of Global Optimization in 2017.



Ya-Feng LiuYa-Feng Liu received the B.Sc. degree in applied mathematics from Xidian University, Xi'an, China, in 2007, and the Ph.D. degree in computational mathematics from the Chinese Academy of Sciences (CAS), Beijing, China, in 2012. During his Ph.D. study, he was supported by the Academy of Mathematics and Systems Science (AMSS), CAS, to visit Professor Zhi-Quan (Tom) Luo at the University of Minnesota (Twins Cities) from 2011 to 2012.

He joined the Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, Beijing, China, in 2012, where he became an Associate Professor in 2018. His main research interests are nonlinear optimization and its applications to signal processing, wireless communications, and machine learning.

Dr. Liu received the Best Paper Award from the IEEE International Conference on Communications (ICC) in 2011, the 15th IEEE ComSoc Asia-Pacific Outstanding Young Researcher Award in 2020, and the Science and Technology Award for Young Scholars from China Society for Industrial and Applied Mathematics in 2022. Students supervised by him won the Best Student Paper Award of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) in 2022. He currently serves as an Associate Editor for the IEEE Transactions on Signal Processing, the IEEE Signal Processing Letters, and the Journal of Global Optimization. He served as an Editor for the IEEE Transactions on Wireless Communications (2019--2022). He is an elected member of the Signal Processing for Communications and Networking Technical Committee (SPCOM-TC) of the IEEE Signal Processing Society (2020--2022 and 2023--2025).


Jing ZhouJing Zhou received the B.Sc in Statistics from Nankai University in 2009 and the Ph. D. in Operational Research and Control Theory from Tsinghua University in 2014. She is a member of China Society for Industrial and Applied Mathematics and was recently classified as high-level talent in Zhejiang Province.

She is currently an Assistant Professor with the Department of Applied Mathematics at Zhejiang University of Technology, located in Hangzhou, China. Her research interests include nonlinear optimization, linear conic programming, semidefinite programming relaxation, algorithms design and signal processing. Her research provides insights on how to use a simultaneous diagonalization based second-order cone relaxation to solve linear complementarity problems, as well as non-convex quadratic programming with convex quadratic constraints.

Dr. Zhou is an active researcher. She has authored and co-authored over a dozen papers. During the past 9 years, Zhou has supervised more than 15 B.S. and M.S. theses in the field of Optimization. Her other contributions to the Mathematics community include peer-reviews for various journals. She also serves as PI for many research projects such as National Natural Science Foundation of China (NSFC) and Zhejiang Provincial Natural Science Foundation of China.