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Robust and continuous metric subregularity for linear inequality systems

Author

Listed:
  • J. Camacho

    (Miguel Hernández University of Elche)

  • M. J. Cánovas

    (Miguel Hernández University of Elche)

  • M. A. López

    (University of Alicante
    CIAO, Federation University)

  • J. Parra

    (Miguel Hernández University of Elche)

Abstract

This paper introduces two new variational properties, robust and continuous metric subregularity, for finite linear inequality systems under data perturbations. The motivation of this study goes back to the seminal work by Dontchev, Lewis, and Rockafellar (2003) on the radius of metric regularity. In contrast to the metric regularity, the unstable continuity behavoir of the (always finite) metric subregularity modulus leads us to consider the aforementioned properties. After characterizing both of them, the radius of robust metric subregularity is computed and some insights on the radius of continuous metric subregularity are provided.

Suggested Citation

  • J. Camacho & M. J. Cánovas & M. A. López & J. Parra, 2023. "Robust and continuous metric subregularity for linear inequality systems," Computational Optimization and Applications, Springer, vol. 86(3), pages 967-988, December.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:3:d:10.1007_s10589-022-00437-0
    DOI: 10.1007/s10589-022-00437-0
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    References listed on IDEAS

    as
    1. M. J. Cánovas & R. Henrion & M. A. López & J. Parra, 2016. "Outer Limit of Subdifferentials and Calmness Moduli in Linear and Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 925-952, June.
    2. Hui Hu, 2005. "Characterizations of the Strong Basic Constraint Qualifications," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 956-965, November.
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