IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v185y2020i3d10.1007_s10957-020-01679-w.html
   My bibliography  Save this article

Robust Farkas-Minkowski Constraint Qualification for Convex Inequality System Under Data Uncertainty

Author

Listed:
  • Xiao-Bing Li

    (Chongqing Jiaotong University)

  • Suliman Al-Homidan

    (King Fahd University of Petroleum and Minerals)

  • Qamrul Hasan Ansari

    (King Fahd University of Petroleum and Minerals
    Aligarh Muslim University)

  • Jen-Chih Yao

    (China Medical University)

Abstract

The Farkas-Minkowski constraint qualification is an important concept within the theory and applications of mathematical programs with inequality constraints. In this paper, we mainly deal with the robust version of Farkas-Minkowski constraint qualification for convex inequality system under data uncertainty. We prove that the existence of robust global error bound is a sufficient condition for ensuring robust Farkas-Minkowski constraint qualification for convex inequality system in face of data uncertainty, where the uncertain data belong to a prescribed compact and convex uncertainty set. Moreover, we show that the converse is true for convex quadratic inequality system, when the uncertain data belong to a scenario uncertainty set.

Suggested Citation

  • Xiao-Bing Li & Suliman Al-Homidan & Qamrul Hasan Ansari & Jen-Chih Yao, 2020. "Robust Farkas-Minkowski Constraint Qualification for Convex Inequality System Under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 785-802, June.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:3:d:10.1007_s10957-020-01679-w
    DOI: 10.1007/s10957-020-01679-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01679-w
    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/s10957-020-01679-w?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. A. Charnes & W. W. Cooper & K. Kortanek, 1965. "On Representations of Semi-Infinite Programs which Have No Duality Gaps," Management Science, INFORMS, vol. 12(1), pages 113-121, September.
    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. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    2. Qinghong Zhang, 2008. "Uniform LP duality for semidefinite and semi-infinite programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 205-213, June.
    3. M. A. Goberna & V. Jornet & R. Puente & M. I. Todorov, 1999. "Analytical Linear Inequality Systems and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 95-119, October.
    4. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    5. Jerez, Belen, 2003. "A dual characterization of incentive efficiency," Journal of Economic Theory, Elsevier, vol. 112(1), pages 1-34, September.
    6. Belen Jerez, 2000. "General Equilibrium with Asymmetric Information: A Dual Approach," Econometric Society World Congress 2000 Contributed Papers 1497, Econometric Society.
    7. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    8. Qinghong Zhang, 2017. "Strong Duality and Dual Pricing Properties in Semi-Infinite Linear Programming: A non-Fourier–Motzkin Elimination Approach," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 702-717, December.
    9. 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.
    10. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    11. M. A. Goberna & M. A. López, 2017. "Recent contributions to linear semi-infinite optimization," 4OR, Springer, vol. 15(3), pages 221-264, September.

    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:185:y:2020:i:3:d:10.1007_s10957-020-01679-w. 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.