IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v171y2016i2d10.1007_s10957-016-0952-8.html
   My bibliography  Save this article

A Strong Metric Subregularity Analysis of Nonsmooth Mappings Via Steepest Displacement Rate

Author

Listed:
  • Amos Uderzo

    (University of Milano-Bicocca)

Abstract

In this paper, a systematic study of the strong metric subregularity property of mappings is carried out by means of a variational tool, called steepest displacement rate. With the aid of this tool, a simple characterization of strong metric subregularity for multifunctions acting in metric spaces is formulated. The resulting criterion is shown to be useful for establishing stability properties of the strong metric subregularity in the presence of perturbations, as well as for deriving various conditions, enabling one to detect such a property in the case of nonsmooth mappings. Some of these conditions, involving several nonsmooth analysis constructions, are then applied in studying the isolated calmness property of the solution mapping to parameterized generalized equations.

Suggested Citation

  • Amos Uderzo, 2016. "A Strong Metric Subregularity Analysis of Nonsmooth Mappings Via Steepest Displacement Rate," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 573-599, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0952-8
    DOI: 10.1007/s10957-016-0952-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-0952-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-016-0952-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. S. Adly & R. Cibulka, 2014. "Quantitative Stability of a Generalized Equation," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 90-110, January.
    2. A. J. Zaslavski, 2014. "An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 649-664, August.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexander Y. Kruger, 2016. "Nonlinear Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 820-855, December.
    2. Matthieu Maréchal, 2018. "Metric Subregularity in Generalized Equations," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 541-558, March.
    3. Huynh Ngai & Nguyen Huu Tron & Michel Théra, 2016. "Directional Hölder Metric Regularity," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 785-819, December.
    4. Samir Adly, 2019. "A Coderivative Approach to the Robust Stability of Composite Parametric Variational Systems: Applications in Nonsmooth Mechanics," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 62-90, January.
    5. Nguyen Xuan Duy Bao & Phan Quoc Khanh & Nguyen Minh Tung, 2022. "Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(1), pages 205-228, September.
    6. Thai Doan Chuong, 2019. "Stability of Implicit Multifunctions via Point-Based Criteria and Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 920-943, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0952-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.