IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-1-4614-8615-2_3.html
   My bibliography  Save this book chapter

Separable Reduction of Metric Regularity Properties

In: Constructive Nonsmooth Analysis and Related Topics

Author

Listed:
  • A. D. Ioffe

    (Department of Mathematics, Technion)

Abstract

We show that for a set-valued mapping F: X → Y between Banach spaces the property of metric regularity near a point of its graph is separably determined in the sense that it holds, provided for any separable subspaces L 0 ⊂ X and M ⊂ Y, containing the corresponding components of the point, there is a separable subspace L ⊂ X containing L 0 such that the mapping whose graph is the intersection of the graph of F with L × M (restriction of F to L × M) is metrically regular near the same point. Moreover, it is shown that the rates of regularity of the mapping near the point can be recovered from the rates of such restrictions.

Suggested Citation

  • A. D. Ioffe, 2014. "Separable Reduction of Metric Regularity Properties," Springer Optimization and Its Applications, in: Vladimir F. Demyanov & Panos M. Pardalos & Mikhail Batsyn (ed.), Constructive Nonsmooth Analysis and Related Topics, edition 127, pages 25-37, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-8615-2_3
    DOI: 10.1007/978-1-4614-8615-2_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:spochp:978-1-4614-8615-2_3. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.