Abstract:
Bilevel optimization (BO), which concerns optimal decision making in processes that involve an upper-level decision maker (the leader) and a lower-level decision maker (the follower), has attracted much interest lately due to its many applications in machine learning and signal processing. One of the current research directions is the design of efficient iterative methods with complexity guarantees for computing approximate stationary points of structured BO problems. However, existing results in this direction either make the restrictive assumption that the lower-level solution mapping is a singleton or only establish the tractability of rather weak stationarity concepts. In this talk, we introduce a new regularity property of set-valued mappings called set smoothness and show that if a BO problem has, among other things, a set-smooth lower-level solution mapping, then the task of finding an approximate Clarke stationary point of the problem is tractable. Our results significantly sharpen those in the literature and suggest several directions for further research.

Bio:

Anthony Man-Cho So joined The Chinese University of Hong Kong (CUHK) in 2007. He is currently Dean of the Graduate School, Acting 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.

Dr. So is a Fellow of IEEE and a Fellow of the Hong Kong Institution of Engineers. He is the recipient of a number of research and teaching awards, including the 2024 INFORMS Computing Society Prize, the SIAM Review SIGEST Award in 2024, the 2018 IEEE Signal Processing Society Best Paper Award, the 2015 IEEE Signal Processing Society Signal Processing Magazine Best Paper Award, the 2014 IEEE Communications Society Asia-Pacific Outstanding Paper Award, and the 2010 INFORMS Optimization Society Optimization Prize for Young Researchers, as well as the 2022 University Grants Committee (UGC) Teaching Award (General Faculty Members Category), the 2022 University Education Award, and the 2013 CUHK Vice-Chancellor’s Exemplary Teaching Award. Dr. So currently serves on the editorial boards of Journal of Global Optimization, Mathematical Programming, Mathematics of Operations Research, Open Journal of Mathematical Optimization, and Optimization Methods and Software.