IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v82y2015i2p123-142.html
   My bibliography  Save this article

First order solutions in conic programming

Author

Listed:
  • Mirjam Dür
  • Bolor Jargalsaikhan
  • Georg Still

Abstract

We study the order of maximizers in linear conic programming (CP) as well as stability issues related to this. We do this by taking a semi-infinite view on conic programs: a linear conic problem can be formulated as a special instance of a linear semi-infinite program (SIP), for which characterizations of the stability of first order maximizers are well-known. However, conic problems are highly special SIPs, and therefore these general SIP-results are not valid for CP. We discuss the differences between CP and general SIP concerning the structure and results for stability of first order maximizers, and we present necessary and sufficient conditions for the stability of first order maximizers in CP. Copyright The Author(s) 2015

Suggested Citation

  • Mirjam Dür & Bolor Jargalsaikhan & Georg Still, 2015. "First order solutions in conic programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 123-142, October.
    • Handle: RePEc:spr:mathme:v:82:y:2015:i:2:p:123-142
    DOI: 10.1007/s00186-015-0513-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-015-0513-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-015-0513-1?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. M. Goberna & M. Todorov & V. Vera de Serio, 2012. "On stable uniqueness in linear semi-infinite optimization," Journal of Global Optimization, Springer, vol. 53(2), pages 347-361, June.
    2. Jérôme Bolte & Aris Daniilidis & Adrian S. Lewis, 2011. "Generic Optimality Conditions for Semialgebraic Convex Programs," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 55-70, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Oliver Stein & Maximilian Volk, 2023. "Generalized Polarity and Weakest Constraint Qualifications in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1156-1190, September.

    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. Mirjam Dür & Bolor Jargalsaikhan & Georg Still, 2017. "Genericity Results in Linear Conic Programming—A Tour d’Horizon," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 77-94, January.
    2. Madeleine Udell & Stephen Boyd, 2016. "Bounding duality gap for separable problems with linear constraints," Computational Optimization and Applications, Springer, vol. 64(2), pages 355-378, June.
    3. Jae Hyoung Lee & Gue Myung Lee & Tiến-Sơn Phạm, 2018. "Genericity and Hölder Stability in Semi-Algebraic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 56-77, July.
    4. Samuel Vaiter & Charles Deledalle & Jalal Fadili & Gabriel Peyré & Charles Dossal, 2017. "The degrees of freedom of partly smooth regularizers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 791-832, August.
    5. Gue Myung Lee & Tiến-Sơn Phạm, 2016. "Stability and Genericity for Semi-algebraic Compact Programs," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 473-495, May.

    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:mathme:v:82:y:2015:i:2:p:123-142. 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.