报告人：李冲（浙江大学）
时间：10月13日，14:00-16:00
地点：36-510
摘要：In the talk, we investigate a linearized proximal algorithm (LPA) for solving a convex composite optimization problem, including the constant and the adaptive stepsizes. Each iteration of the LPA is a proximal minimization of the convex composite function with the inner function being linearized at the current iterate. The LPA has the attractive computational advantage that the solution of each subproblem is a singleton, which avoids the difficulty as in the Gauss-Newton method (GNM) of finding a solution with minimum norm among the set of minima of its subproblem, while it still maintains the same local convergence rate as that of the GNM. We also propose a globalization strategy for the LPA based on a backtracking line-search and an inexact version of the LPA. Under the assumptions of local weak sharp minima of order $p (p \geq 1)$ 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. 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 some popular algorithms for relevant problems.
报告人简介：李冲，现任浙江大学数学科学学院教授，博士生导师。目前主要从事非光滑分析、数值泛函分析、最优化理论和方法等领域的研究。特别在黎曼流形上的优化理论和算法，Banach空间中的约束规范等领域的研究在国际上有比较大的影响。部分成果获得省部级自然科学三等奖。先后主持国家自然科学基金、或以主研人员参加国家自然科学基金重大和重点项目等10余项的研究，同时主持和参加了多项西班牙及南非国家自然科学基金等项目的研究。在科学出版社“现代数学基础丛书”出版专著1部，在SCI期刊上发表论文100余篇， 特别是在优化理论，科学计算以及机器学习领域的顶级刊物SIAM J Optim.，SIAM J. Control Optim.，Math. Program，SIAM J Numer Anal以及JMLR等发表学术论文30余篇。 于1992年享受国务院政府特殊津贴、获原商业部有突出贡献的中青年专家、江苏省青蓝工程优秀骨干教师。教育部优秀骨干教师，江苏省第七届青年科学家等称号。 2004年获教育部首届新世纪优秀人才计划资助。
