The Lipschitz-like Property Relative to a Set with Applications 相对一个集合的类利普希兹性质及其应用
Professor Xiaoqi Yang (The Hong Kong Polytechnic University) 杨晓琪教授（香港理工大学）
Stability analysis of set-valued mappings is to determine intuitively verifiable conditions to guarantee that the accuracy of the solutions obtained increases with the degree of approximation of the initial data. The literature on the subject is vast when the study is of global nature. In many applications of compressive sensing, machine learning, pattern analysis and graphical modeling, the underlying data are related by an under-determined linear measurement. The solution set for the optimization problem of recovering the sparse solution of under-determined linear measurement satisfies a so-called calmness property related to the positive half line. This property may not be sufficient for some practical application. In this paper, we will study the Lipschitz-like property of this solution set relative to the positive half line. We will develop a general framework for the Lipschitz-like property relative to a set of a set-valued mapping and obtain some necessary conditions and some sufficient conditions when the set is closed. If the set is closed and convex, we will develop a general Mordukhovich criterion by virtue of a projectional coderivative.
Professor Xiaoqi Yang is a professor at the Hong Kong Polytechnic University since 2005. His research interests include nonsmooth analysis, vector optimization and financial optimization. He publishes papers in high-quality journals, such as Management Science, Operations Research, Mathematical Programming, SIAM Journal on Optimization.
杨晓琪教授自2005年起是香港理工大学的教授，他的研究兴趣包括非光滑分析，向量优化以及金融优化。他在高质量期刊发表很多论文，报告《Management Science》, 《Operations Research》, 《Mathematical Programming》, 《SIAM Journal on Optimization》.