题　　目：A Unified Primal-Dual Algorithm Framework for Inequality Constrained Problems

　　报 告 人：文再文 教授

　　报告时间：2022年9月13日10：00-11：30

　　报告地点：线上腾讯会议号　917 570 504

　　报告人简介：

　　文再文，北京大学北京国际数学研究中心教授，主要研究最优化算法与理论及其在机器学习、人工智能中的应用。2016年获中国青年科技奖。现为中国运筹学会常务理事中国运筹学会数学规划分会副理事长。

　　报告内容：

　　In this talk, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers many existing algorithms such as PDHG, Chambolle-Pock (CP), GDA, OGDA and linearized ALM, but also guides us to design a new efficient algorithm called Simi-OGDA (SOGDA). Second, it enables us to study the role of the augmented penalty term in the convergence analysis. Under properly designed step sizes and penalty term, our unified framework preserves the O(1/N) ergodic convergence while not requiring any prior knowledge about the magnitude of the optimal Lagrangian multiplier. Numerical experiments on linear programming, L1 minimization problem, and multi-block basis pursuit problem demonstrate the efficiency of our methods.