6月10日 Yangyang Xu博士学术报告

发布时间:2026-05-27

报告题目：Alternating Direction Method of Multipliers for nonlinear constrained convex problems

主讲人：Dr. Yangyang Xu, Rensselaer Polytechnic Institute 

报告时间：2026年6月10日（周三），15:00-16:00

报告地点：计算机学院A327

主持人：王晓教授

摘要：

We study a class of structured convex optimization problems, which have a two-block separable objective and nonlinear functional constraints as well as affine constraints that couple the two block variables. Such problems naturally arise from distributed resource allocation and constrained machine learning. To achieve high communication efficiency for the distributed applications, we propose a nonlinear alternating direction method of multipliers  (NL-ADMM) that preserves the classical splitting structure while accommodating general convex functional constraints. Unlike existing ADMM variants for nonconvex constrained problems, the proposed method does not require smoothness of the objective functions or differentiability of the constraint mapping, by leveraging convexity of the considered problem. We establish global convergence and an ergodic $\mathcal{O}(1/k)$ convergence rate of NL-ADMM by assuming the existence of a KKT solution. The results extend those of ADMM for linearly constrained convex problems. Numerical experiments are conducted on two representative distributed tasks. The results on numerous instances demonstrate that NL-ADMM can achieve (in many cases) 100x higher communication efficiency than the classic augmented Lagrangian method and nearly 2x higher than the Douglas-Rachford operator splitting method, making the new method well suited for large-scale distributed learning systems.

主讲人简介：

Yangyang Xu is an Associate Professor in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute. He received his B.S. in Computational Mathematics from Nanjing University in 2007, his M.S. in Operations Research from the Chinese Academy of Sciences in 2010, and his Ph.D. in Computational and Applied Mathematics from Rice University in 2014. His research focuses on optimization theory and algorithms and their applications in machine learning, statistics, and signal processing. His recent work centers on stochastic optimization, robust machine learning, large-scale constrained optimization, and distributed optimization. He currently serves as an Associate Editor for Mathematics of Operations Research.