School of Mathematical Sciences Academic Report [2025] 057

(High-Level University Construction Series Report No. 1079)

Lecture Title: Revisiting the Proximity Operator of the $\ell_1$ over $\ell_2$ Function

Speaker: Prof. Lixin Shen (Syracuse University, USA)

Date & Time: 4:30 PM – 5:30 PM, June 25, 2025

Venue: Room 514, Convergence Stars Building

Abstract: In this talk, we characterize the proximity operator of the $\ell_1/\ell_2$ function. By reformulating the underlying optimization problem over a smooth manifold, we establish that its solution corresponds to a local non-global minimizer of a quadratic function constrained to the unit sphere. We further develop dedicated algorithms to compute this proximity operator exactly. (Joint work with Guohui Song)

Biography: Lixin Shen is a professor of mathematics at Syracuse University, specializing in applied mathematics. His research focuses on optimization, variational methods, signal and image processing, and sparsity-driven modeling. He has made significant contributions to the mathematical foundations of inverse problems and regularization techniques, and actively collaborates with researchers in areas such as medical imaging and machine learning.

Professor Shen received his B.S. and M.S. degrees in mathematics from Peking University, and earned his Ph.D. in Mathematics from Sun Yat-sen University in 1996. At Syracuse, he teaches undergraduate and graduate courses and mentors students in both theoretical and applied research.

Invited by: Prof. Jian Lu

All faculty and students are welcome!

School of Mathematical Sciences

June 25, 2025