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学术报告:A Unified Convergence Analysis of a Second-Order Method of Multipliers for Nonlinear Conic Programming

2020年12月10日 11:22  点击:[]

湖南大学陈亮副教授学术报告

 

一、报告题目:A Unified Convergence Analysis of a Second-Order Method of Multipliers for Nonlinear Conic Programming

二、报告人:陈亮副教授—湖南大学 数学学院

三、报告时间:2020年1212日星期六下午15:00

四、报告地点:数学与统计学院会议室80602

五、报告摘要:In this talk, we will introducea unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the conventional nonlinear conic optimization problems. Specifically, the algorithm that we investigated incorporates a specially designed nonsmooth (generalized) Newton step to furnish a second-order update of the multipliers in the augmented Lagrangian method. We show in a unified fashion that under a few abstract assumptions, the proposed method is locally convergent and possesses a (nonasymptotic) superlinear convergence rate, even though the penalty parameter is fixed and/or the strict complementarity fails. Subsequently, we demonstrate that, for the three typical scenarios, i.e., the classic nonlinear programming, the nonlinear second-order cone programming, and the nonlinear semidefinite programming, these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that were assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity.

 

报告人简介: 陈亮博士现任湖南大学数学学院教授,信息与计算科学系副主任研究方向是数学优化,主要研究最优化问题求解的计算方法和数值实现。先后2009年和2016年在湖南大学数学学院获学士学位和获博士学位,博士在读期间在新加波国立大学(国家公派)联合培养2017-2019年先后在新加坡国立大学数学系和香港理工大学应用数学系从事博士后研究。目前已在《Mathematical ProgrammingMathematical ProgrammingComputation数学优专业期刊发表论文篇,主持国家自然科学基金青年项目、湖南省自然科学基金青年项目和湖南大学青年教师托举计划专项基金美国数学会评论员以及湖南省计算数学与应用软件学会理事。

欢迎感兴趣的老师和同学参加!

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