江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：Finding Cheeger cuts via 1-Laplacian of graphs
報告人：朱炜教授
報告時間：2024年6月13日（周四）上午9:00-10:00
報告地點：伟德bvA302
主持人：楊文莉
報告摘要：Finding Cheeger cuts of graphs is an NP-hard problem, and one often resorts to approximate solutions. In the literature, spectral graph theory provides the most popular approaches for obtaining such approximate solutions. Recently, Prof. K.C. Chang introduced a novel nonlinear spectral graph theory and proved that the seek of Cheeger cuts is equivalent to solving a constrained optimization problem. However, this resulting optimization problem is also very challenging as it involves a non-differentiable function over a non-convex set that is composed of simplex cells of different dimensions. In this talk, we will discuss an ADMM algorithm for solving this optimization problem and provide some convergence analysis. Experimental results will be presented for typical graphs, including Petersen's graph and Cockroach graphs, the well-known Zachary karate club graph, and some preliminary applications in material sciences.
報告人簡介：Zhu Wei received the B.S. degree in mathematics from Tsinghua University in 1994, the M.S. degree in mathematics from Peking University in 1999, and the Ph.D. degree in applied mathematics from UCLA in 2004. He is currently a professor in the Department of Mathematics at the University of Alabama, Tuscaloosa. His research interests include PDE methods for image processing and data sciences.