IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v162y2014i2d10.1007_s10957-013-0486-2.html
   My bibliography  Save this article

Enhanced Efficiency in Multi-objective Optimization

Author

Listed:
  • Y. Jiang

    (Nanjing University of Information Science and Technology)

  • S. Deng

    (Northern Illinois University)

Abstract

For a given multi-objective optimization problem, we introduce and study the notion of α-proper efficiency. We give two characterizations of such proper efficiency: one is in terms of exact penalization and the other is in terms of stability of associated parametric problems. Applying the aforementioned characterizations and recent results on global error bounds for inequality systems, we obtain verifiable conditions for α-proper efficiency. For a large class of polynomial multi-objective optimization problems, we show that any efficient solution is α-properly efficient under some mild conditions. For a convex quadratically constrained multi-objective optimization problem with convex quadratic objective functions, we show that any efficient solution is α-properly efficient with a known estimate on α whenever its constraint set is bounded. Finally, we illustrate our achieved results with examples, and give an example to show that such an enhanced efficiency property may not hold for multi-objective optimization problems involving C ∞-functions as objective functions.

Suggested Citation

  • Y. Jiang & S. Deng, 2014. "Enhanced Efficiency in Multi-objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 577-588, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0486-2
    DOI: 10.1007/s10957-013-0486-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0486-2
    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/s10957-013-0486-2?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. Deng, 1998. "On Efficient Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 201-209, January.
    2. Alexander J. Zaslavski, 2010. "Optimization on Metric and Normed Spaces," Springer Optimization and Its Applications, Springer, number 978-0-387-88621-3, 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. César Gutiérrez & Rubén López & Vicente Novo, 2014. "Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 515-547, August.
    2. César Gutiérrez & Rubén López, 2020. "On the Existence of Weak Efficient Solutions of Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 880-902, June.
    3. S. Deng, 2010. "Boundedness and Nonemptiness of the Efficient Solution Sets in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 29-42, January.
    4. 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.
    5. Dingtao Peng & Jian Yu & Naihua Xiu, 2013. "Generic uniqueness theorems with some applications," Journal of Global Optimization, Springer, vol. 56(2), pages 713-725, June.
    6. D. T. Peng & J. Yu & N. H. Xiu, 2012. "Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 165-179, October.
    7. Rubén López, 2013. "Variational convergence for vector-valued functions and its applications to convex multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 1-34, August.
    8. Yarui Duan & Liguo Jiao & Pengcheng Wu & Yuying Zhou, 2022. "Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 148-171, October.
    9. Enrico Biffis & Erik Chavez, 2017. "Satellite Data and Machine Learning for Weather Risk Management and Food Security," Risk Analysis, John Wiley & Sons, vol. 37(8), pages 1508-1521, August.

    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:162:y:2014:i:2:d:10.1007_s10957-013-0486-2. 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.