学术报告

题      目： Linearized proximal algorithms with adaptive step sizes for convex composite optimization with applications

报  告  人：李冲  教授  (邀请人：谭露琳 )

                                  浙江大学

时      间：2022-04-22  09：30-11：30

腾讯会议：123-791-207（密码：0830）

报告人简介:

       李冲，浙江大学数学系教授，博士生导师。主要从事非线性优化理论与计算、数值泛函分析、数值代数、稀疏优化及其应用、机器学习等领域的研究。先后主持国家自然科学基金及省部级项目等近二十项，出版专著1部，在SCI期刊上发表论文近200篇， 特别是在优化理论和计算数学的顶级刊物SIAM J Optim., Math. Program，SIAM J. Control Optim.以及SIAM J.Numer. Anal上发表论文近30篇。1992年起享受国务院政府特殊津贴，获浙江省教委科技进步奖一、二等奖等奖励，原商业部有突出贡献的中青年专家、江苏省第七届青年科学家等，2004年获教育部首届新世纪优秀人才计划资助。

摘      要：

       In this talk, we will propose an inexact linearized proximal algorithm with an adaptive stepsize, together with its globalized version based on the back-tracking line-search, to solve the convex composite optimization problem.
Under the assumptions of local weak sharp minima of order p (p>=1) for the outer convex function and a quasi-regularity condition for the inclusion problem associated to the inner function,  we establish the superlinear/quadratic convergence results for the proposed algorithms. Compared to the linearized proximal algorithms with a constant stepsize proposed in our paper, our algorithms own broader applications and higher convergence rates. Numerical applications to the nonnegative inverse eigenvalue problem and the wireless sensor network localization problem indicate that the proposed algorithms are more efficient and robust, and outperform the algorithms proposed in [1] and some popular algorithms for relevant problems.