IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v107y2000i2d10.1023_a1026433520314.html
   My bibliography  Save this article

Optimization of the Norm of a Vector-Valued DC Function and Applications

Author

Listed:
  • R. Blanquero

    (Universidad de Sevilla)

  • E. Carrizosa

    (Universidad de Sevilla)

Abstract

In this paper, we show that a DC representation can be obtained explicitly for the composition of a gauge with a DC mapping, so that the optimization of certain functions involving terms of this kind can be made by using standard DC optimization techniques. Applications to facility location theory and multiple-criteria decision making are presented.

Suggested Citation

  • R. Blanquero & E. Carrizosa, 2000. "Optimization of the Norm of a Vector-Valued DC Function and Applications," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 245-260, November.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:2:d:10.1023_a:1026433520314
    DOI: 10.1023/A:1026433520314
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1026433520314
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1026433520314?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. Y. P. Aneja & M. Parlar, 1994. "Technical Note—Algorithms for Weber Facility Location in the Presence of Forbidden Regions and/or Barriers to Travel," Transportation Science, INFORMS, vol. 28(1), pages 70-76, February.
    2. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    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. Blanquero, R. & Carrizosa, E. & Hendrix, E.M.T., 2011. "Locating a competitive facility in the plane with a robustness criterion," European Journal of Operational Research, Elsevier, vol. 215(1), pages 21-24, November.
    2. Rafael Blanquero & Emilio Carrizosa, 2010. "On the norm of a dc function," Journal of Global Optimization, Springer, vol. 48(2), pages 209-213, October.
    3. Hoai An Le Thi & Vinh Thanh Ho & Tao Pham Dinh, 2019. "A unified DC programming framework and efficient DCA based approaches for large scale batch reinforcement learning," Journal of Global Optimization, Springer, vol. 73(2), pages 279-310, February.
    4. Rafael Blanquero & Emilio Carrizosa & Pierre Hansen, 2009. "Locating Objects in the Plane Using Global Optimization Techniques," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 837-858, November.
    5. Rafael Blanquero & Emilio Carrizosa, 2013. "Solving the median problem with continuous demand on a network," Computational Optimization and Applications, Springer, vol. 56(3), pages 723-734, December.

    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. Shota Takahashi & Mituhiro Fukuda & Mirai Tanaka, 2022. "New Bregman proximal type algorithms for solving DC optimization problems," Computational Optimization and Applications, Springer, vol. 83(3), pages 893-931, December.
    2. Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2014. "Time Consistent Behavior Portfolio Policy for Dynamic Mean-Variance Formulation," Papers 1408.6070, arXiv.org, revised Aug 2015.
    3. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2015. "On a Smooth Dual Gap Function for a Class of Player Convex Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 659-685, August.
    4. Boglárka G.-Tóth & Kristóf Kovács, 2016. "Solving a Huff-like Stackelberg location problem on networks," Journal of Global Optimization, Springer, vol. 64(2), pages 233-247, February.
    5. Rafael Blanquero & Emilio Carrizosa & Amaya Nogales-Gómez & Frank Plastria, 2014. "Single-facility huff location problems on networks," Annals of Operations Research, Springer, vol. 222(1), pages 175-195, November.
    6. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    7. M. Bierlaire & M. Thémans & N. Zufferey, 2010. "A Heuristic for Nonlinear Global Optimization," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 59-70, February.
    8. Andreas Löhne & Andrea Wagner, 2017. "Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver," Journal of Global Optimization, Springer, vol. 69(2), pages 369-385, October.
    9. N. V. Thoai, 2000. "Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 331-354, November.
    10. Jean-Paul Penot, 2011. "The directional subdifferential of the difference of two convex functions," Journal of Global Optimization, Springer, vol. 49(3), pages 505-519, March.
    11. Xiangyang Huang & LiGuo Huang, 2023. "Spreading Points Using Gradient and Tabu," SN Operations Research Forum, Springer, vol. 4(2), pages 1-11, June.
    12. Mounir El Maghri, 2015. "( $$\epsilon $$ ϵ -)Efficiency in difference vector optimization," Journal of Global Optimization, Springer, vol. 61(4), pages 803-812, April.
    13. Kathrin Klamroth & Margaret M. Wiecek, 2002. "A Bi-Objective Median Location Problem With a Line Barrier," Operations Research, INFORMS, vol. 50(4), pages 670-679, August.
    14. Massol, Olivier & Banal-Estañol, Albert, 2014. "Export diversification through resource-based industrialization: The case of natural gas," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1067-1082.
    15. M. V. Dolgopolik, 2020. "New global optimality conditions for nonsmooth DC optimization problems," Journal of Global Optimization, Springer, vol. 76(1), pages 25-55, January.
    16. Naghavi, Mostafa & Roshdi, Israfil & Arjomandi, Amir & Margaritis, Dimitris, 2023. "Some comments on Russell graph efficiency measures in data envelopment analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 306(1), pages 494-497.
    17. Amiri-Aref, Mehdi & Farahani, Reza Zanjirani & Hewitt, Mike & Klibi, Walid, 2019. "Equitable location of facilities in a region with probabilistic barriers to travel," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 66-85.
    18. Simeon vom Dahl & Andreas Löhne, 2020. "Solving polyhedral d.c. optimization problems via concave minimization," Journal of Global Optimization, Springer, vol. 78(1), pages 37-47, September.
    19. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    20. Masashi Miyagawa, 2017. "Continuous location model of a rectangular barrier facility," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 95-110, April.

    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:107:y:2000:i:2:d:10.1023_a:1026433520314. 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.