Optimal Error Bounds in the Absence of Constraint Qualifications with Applications to p-Cones and Beyond

• 成果类型: Article
• 署名作者: Lindstrom, Scott B.; Lourenco, Bruno F.; Pong, Ting Kei
• 署名单位: Curtin University; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0135
• 发表日期: 2025
• 关键词: facial reduction; INEQUALITY; Duality

摘要

We prove tight Holderian lderian error bounds for all p -cones. Surprisingly, the exponents differ in several ways from those that have been previously conjectured. Moreover, they illuminate p -cones as a curious example of a class of objects that possess properties in three dimensions that they do not in four or more. Using our error bounds, we analyse least squares problems with p -norm regularization, where our results enable us to compute the corresponding Kurdyka-& Lstrok;ojasiewicz exponents for previously inaccessible values of p . Another application is a (relatively) simple proof that most p -cones are neither self -dual nor homogeneous. Our error bounds are obtained under the framework of facial residual functions, and we expand it by establishing for general cones an optimality criterion under which the resulting error bound must be tight.