学术报告报告题目：Lipschitz-like property relative to a set and the generalized Mordukhovich criterion
报 告 人：杨晓琪 教授（香港理工大学）
报告时间：2020年1月14日（星期二）上午10:00-11:00
报告地点：4号楼 318 室
邀 请 人：潘少华 教授
欢迎广大师生前往！
数学学院
2020年 1 月 10 日
报告摘要：
In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone of a restricted graph of the set-valued mapping. We will obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set by virtue of the projection of the coderivative onto a tangent cone. Furthermore, by introducing a projectional coderivative of set-valued mappings, we establish a verifiable generalized Mordukhovich criterion for the Lipschitz-like property relative to a closed and convex set. We will study the representation of the graphical modulus of a set-valued mapping relative to a closed and convex set by using the outer norm of the corresponding projectional coderivative value. For an extended real-valued function, we will apply the obtained results to investigate its Lipschitz continuity relative to a closed and convex set and the Lipschitz-like property of a level-set mapping relative to a half line.
报告人简介：
杨晓琪1994年博士毕业于澳大利亚新南威尔士大学应用数学系。现任香港理工大学应用数学系教授，博士生导师。主要从事非线性最优化的研究及其在金融问题中的应用，已经在 Management Science，Operations Research，Mathematics of Operations Research，SIAM Journal on Optimization 等国际刊物发表 200 多篇学术论文。撰写了3本专著。先后主持香港政府基金项目 16 项，2000 年获美国 ISI 经典引用奖（ISI Citation Classic Award），2001，2018年获香港理工大学校长杰出贡献奖，2006 年获得重庆市自然科学一等奖。2008年及2014年分别与重庆师范大学合作成功申请到国家重点项目。