This talk explores the Arrow-Hurwicz-Uzawa method, tracing its development from early applications in partial differential equations (PDEs) to modern advancements in optimization, image processing, and scientific computing. We will examine recent refinements for developing GPU-adaptive solvers for huge-scale linear programming and its extension to semidefinite programming arising in quantum information science. The discussion will also highlight the method's integration with deep learning and unrolling techniques for optimal control problems of PDEs, as well as its applications in industry.

Bio of Speaker:

Xiaoming Yuan is a Professor in the Department of Mathematics at The University of Hong Kong. His research spans optimization, optimal control, scientific machine computing, and artificial intelligence. He is well recognized for his fundamental contributions to first-order optimization algorithms, including the Alternating Direction Method of Multipliers (ADMM), primal-dual methods, and proximal point algorithms. He also collaborates extensively with the AI and cloud computing industries. He led the development of the first automatic bandwidth allocation system for the cloud computing sector. His team was honored as a Franz Edelman Award Finalist in 2023. He is a Clarivate Analytics Highly Cited Researcher, a Croucher Senior Research Fellow, and a laurate of Chair of Excellence, Fondation Sciences Mathematiques de Paris, in 2026.