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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Scott B. Lindstrom & Bruno F. Lourenço & Ting Kei Pong, 2025. "Optimal Error Bounds in the Absence of Constraint Qualifications with Applications to p -Cones and Beyond," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1204-1232, May.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:2:p:1204-1232
    DOI: 10.1287/moor.2022.0135
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