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Nonlinear Metric Subregularity

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  • Alexander Y. Kruger

    (Federation University Australia)

Abstract

In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in Kruger (Error bounds and metric subregularity. Optimization 64(1):49–79, 2015). Several primal and dual space local quantitative and qualitative criteria of nonlinear metric subregularity are formulated. The relationships between the criteria are established and illustrated.

Suggested Citation

  • Alexander Y. Kruger, 2016. "Nonlinear Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 820-855, December.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-015-0807-8
    DOI: 10.1007/s10957-015-0807-8
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    References listed on IDEAS

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    1. Marian J. Fabian & René Henrion & Alexander Y. Kruger & Jiří V. Outrata, 2012. "About error bounds in metric spaces," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 33-38, Springer.
    2. Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), 2012. "Operations Research Proceedings 2011," Operations Research Proceedings, Springer, edition 127, number 978-3-642-29210-1, March.
    3. Huynh Van Ngai & Phan Nhat Tinh, 2015. "Metric Subregularity of Multifunctions: First and Second Order Infinitesimal Characterizations," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 703-724, March.
    4. Boris Mordukhovich & Wei Ouyang, 2015. "Higher-order metric subregularity and its applications," Journal of Global Optimization, Springer, vol. 63(4), pages 777-795, December.
    5. O. Cornejo & A. Jourani & C. Zălinescu, 1997. "Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 127-148, October.
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