Although Bregman-type algorithms have been extensively studied over the years, it remains unclear whether existing stationarity measures, often based on Bregman divergence, can distinguish between stationary and non-stationary points. In this talk, we answer this question in the negative. Furthermore, we show that Bregman-type algorithms are unable to escape from a spurious stationary point in finite steps when the initial point is unfavorable, even for convex problems. Our results highlight the inherent distinction between Euclidean and Bregman geometries and call for further investigation of Bregman-type algorithms.

Anthony Man-Cho So received his BSE degree in Computer Science from Princeton University with minors in Applied and Computational Mathematics, Engineering and Management Systems, and German Language and Culture. He then received his MSc degree in Computer Science and his PhD degree in Computer Science with a PhD minor in Mathematics from Stanford University. Dr. So joined The Chinese University of Hong Kong (CUHK) in 2007. He is currently Dean of the Graduate School, Deputy Master of Morningside College, and Professor in the Department of Systems Engineering and Engineering Management. His research focuses on optimization theory and its applications in various areas of science and engineering, including computational geometry, machine learning, signal processing, and statistics.