关于举行罗自炎教授（北京交通大学）学术报告的通知

报告题目: Zero-One Composite Optimization: Lyapunov Exact Penalty and a Globally Convergent Inexact                           Augmented Lagrangian Method

报  告  人: 罗自炎  教授

报告时间: 2023年 12月18 日（星期一）9:00-10:00              

报告地点：37号楼3A02

邀  请  人: 潘少华 教授

数学学院

2023年12月13日

报告摘要：We consider the problem of minimizing the sum of a smooth function and a composition of a zero-one loss function with a linear operator, namely the zero-one composite optimization problem (0/1-COP). It has a vast body of applications, including the support vector machine (SVM), calcium dynamics fitting (CDF), 1-bit compressive sensing (1-bCS) and so on. However, it remains challenging to design a globally convergent algorithm for the original model of 0/1-COP, due to the nonconvex and discontinuous zero-one loss function. We aim to develop an inexact augmented Lagrangian method (IALM) in which the generated whole sequence converges to a local minimizer of 0/1-COP under reasonable assumptions. In the iteration process, IALM performs minimization on a Lyapunov function with an adaptively adjusted multiplier. The involved Lyapunov penalty subproblem is shown to admit the exact penalty theorem for 0/1-COP, provided that the multiplier is optimal in the sense of the proximal type stationarity. An efficient zero-one Bregman alternating linearized minimization (0/1-BALM) algorithm is also designed to achieve an approximate solution of the underlying subproblem in finite steps. Numerical experiments for handling SVM, CDF and 1-bCS demonstrate the satisfactory performance of the proposed method in terms of solution accuracy and time efficiency. 

报告人简介：罗自炎，北京交通大学数学与统计学院教授、博士生导师，中国运筹学会数学规划分会副秘书长，中国运筹学会女性工作委员会委员，中国运筹学会算法软件与应用分会理事。曾访问美国斯坦福大学、新加坡国立大学、香港理工大学、英国南安普顿大学等。主要从事张量优化、稀疏优化及统计优化的理论、算法及应用研究，在SIAM J Optim、Math Program、IEEE Trans Signal Process、J Mach Learn Res、SIAM J Matrix Anal Appl等顶级期刊发表学术论文，合著SIAM出版社英文专著1部，获教育部自然科学奖二等奖、中国运筹学会青年科技奖提名奖、北京市高校本科优秀毕业论文指导教师，入选国家青年拔尖人才计划。