报告题目：Lipschitz continuity of solution multifunctions of the BP-LASSO Problems
主讲人：孟开文教授（西南财经大学）
时间：2026年7月28日（周二）16:00 p.m.
地点：北院卓远楼305会议室
主办单位：统计与数学学院
摘要：
The Lasso and basis pursuit are two fundamental convex optimization problems in machine learning and computer science with three parameters: a regularization scalar, an observation vector, and a data matrix. Relative to the first two parameters, we obtain the Lipschitz continuity of the solution multifunction on its convex domain. When the data matrix of the Lasso also perturbs, where non-polyhedral structure may display, we obtain full characterizations for the Lipschitz continuity of the solution multifunction on the product of a compact and convex set in the space of first two parameters and a neighborhood of the fixed data matrix. Moreover, for the solution multifunction of the Lasso, we show that the Lipschitz continuity implies its single-valuedness. Our analysis is based on polyhedron theory, a sufficient condition that ensures the Lipschitz continuity of a polyhedral multifunction with a convex domain, and an explicit representation of the solution multifunction, where the latter is a consequence of the Lipschitz continuity of the solution multifunction relative to the first two parameters.
主讲人简介：
孟开文，香港理工大学博士，西南财经大学数学学院教授，博士生导师。主要从事最优化理论、算法和应用研究，主持国家自然科学基金青年和面上项目各一项。在SIAM J OPT, OR, MP, JMLR, JGO, JCA等期刊上发表学术论文十余篇。
滇公网安备53010202000350号滇ICP备17008047号 Copyright © 2013 Yunnan University of Finance and Economics All Rights Reserved
