IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v181y2019i1d10.1007_s10957-018-1431-1.html
   My bibliography  Save this article

Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets

Author

Listed:
  • Duong Thi Viet An

    (Thai Nguyen University of Sciences)

  • Jen-Chih Yao

    (China Medical University)

Abstract

This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for $$\varepsilon $$ ε -subdifferentials, we obtain exact formulas for computing the $$\varepsilon $$ ε -subdifferential of the optimal value function. Several illustrative examples are also given.

Suggested Citation

  • Duong Thi Viet An & Jen-Chih Yao, 2019. "Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 126-143, April.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:1:d:10.1007_s10957-018-1431-1
    DOI: 10.1007/s10957-018-1431-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1431-1
    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/s10957-018-1431-1?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. Alberto Seeger, 1996. "Subgradients of Optimal-Value Functions in Dynamic Programming: The Case of Convex Systems Without Optimal Paths," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 555-575, August.
    2. Duong Thi Viet An & Jen-Chih Yao, 2016. "Further Results on Differential Stability of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 28-42, July.
    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. Le Quang Thuy & Nguyen Thi Toan, 2016. "Subgradients of the Value Function in a Parametric Convex Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 43-64, July.
    2. Duong Thi Viet An & Abderrahim Jourani, 2022. "Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 82-96, January.
    3. Kien, B.T. & Liou, Y.C. & Wong, N.-C. & Yao, J.-C., 2009. "Subgradients of value functions in parametric dynamic programming," European Journal of Operational Research, Elsevier, vol. 193(1), pages 12-22, February.
    4. N. H. Chieu & B. T. Kien & N. T. Toan, 2016. "Further Results on Subgradients of the Value Function to a Parametric Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 785-801, March.
    5. N. Toan & J.-C. Yao, 2014. "Mordukhovich subgradients of the value function to a parametric discrete optimal control problem," Journal of Global Optimization, Springer, vol. 58(3), pages 595-612, March.

    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:181:y:2019:i:1:d:10.1007_s10957-018-1431-1. 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.