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

Scott B. Lindstrom (), Bruno F. Lourenço () and Ting Kei Pong ()
Additional contact information
Scott B. Lindstrom: Centre for Optimisation and Decision Science, Curtin University, Bentley, Western Australia 6102, Australia
Bruno F. Lourenço: Department of Fundamental Statistical Mathematics, Institute of Statistical Mathematics, Tokyo 190-8562, Japan
Ting Kei Pong: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, People’s Republic of China

Mathematics of Operations Research, 2025, vol. 50, issue 2, 1204-1232

Abstract: We prove tight Hölderian 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–Łojasiewicz 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.

Keywords: Primary: 90C25; secondary: 52A20; error bounds; facial residual functions; Hölderian error bounds; p -cones (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2022.0135 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:2:p:1204-1232

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().