IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v69y2017i2d10.1007_s10898-017-0519-8.html
   My bibliography  Save this article

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Author

Listed:
  • Andreas Löhne

    (Friedrich Schiller University Jena)

  • Andrea Wagner

    (Vienna University of Economics and Business)

Abstract

A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $$f=g-h$$ f = g - h of two convex functions g and h. In particular, we deal with the special case where one of the two convex functions g or h is polyhedral. In case g is polyhedral, we show that a solution of the DC program can be obtained from a solution of an associated polyhedral projection problem. In case h is polyhedral, we prove that a solution of the DC program can be obtained by solving a polyhedral projection problem and finitely many convex programs. Since polyhedral projection is equivalent to multiple objective linear programming (MOLP), a MOLP solver (in the second case together with a convex programming solver) can be used to solve instances of DC programs with polyhedral component. Numerical examples are provided, among them an application to locational analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0519-8
    DOI: 10.1007/s10898-017-0519-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0519-8
    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/s10898-017-0519-8?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. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. B. Dasarathy & Lee J. White, 1980. "A Maxmin Location Problem," Operations Research, INFORMS, vol. 28(6), pages 1385-1401, December.
    3. László Csirmaz, 2016. "Using multiobjective optimization to map the entropy region," Computational Optimization and Applications, Springer, vol. 63(1), pages 45-67, January.
    4. Richard L. Church & Robert S. Garfinkel, 1978. "Locating an Obnoxious Facility on a Network," Transportation Science, INFORMS, vol. 12(2), pages 107-118, May.
    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. Daniel Ciripoi & Andreas Löhne & Benjamin Weißing, 2018. "A vector linear programming approach for certain global optimization problems," Journal of Global Optimization, Springer, vol. 72(2), pages 347-372, October.
    2. Çağın Ararat & Firdevs Ulus & Muhammad Umer, 2022. "A Norm Minimization-Based Convex Vector Optimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 681-712, August.
    3. 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.
    4. Andrea Wagner, 2019. "Locating a semi-obnoxious facility in the special case of Manhattan distances," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 255-270, October.

    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. Andrea Wagner, 2019. "Locating a semi-obnoxious facility in the special case of Manhattan distances," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 255-270, October.
    2. Heydari, Ruhollah & Melachrinoudis, Emanuel, 2012. "Location of a semi-obnoxious facility with elliptic maximin and network minisum objectives," European Journal of Operational Research, Elsevier, vol. 223(2), pages 452-460.
    3. 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.
    4. 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.
    5. 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.
    6. João Carlos O. Souza & Paulo Roberto Oliveira & Antoine Soubeyran, 2016. "Global convergence of a proximal linearized algorithm for difference of convex functions," Post-Print hal-01440298, HAL.
    7. 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.
    8. Pelegrín, Mercedes & Xu, Liding, 2023. "Continuous covering on networks: Improved mixed integer programming formulations," Omega, Elsevier, vol. 117(C).
    9. Balakrishnan, K. & Changat, M. & Mulder, H.M. & Subhamathi, A.R., 2011. "Consensus Strategies for Signed Profiles on Graphs," Econometric Institute Research Papers EI2011-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Aras Selvi & Aharon Ben-Tal & Ruud Brekelmans & Dick den Hertog, 2022. "Convex Maximization via Adjustable Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2091-2105, July.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Zhili Ge & Zhongming Wu & Xin Zhang & Qin Ni, 2023. "An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 821-844, August.
    16. Rainer Burkard & Jafar Fathali, 2007. "A polynomial method for the pos/neg weighted 3-median problem on a tree," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 229-238, April.
    17. Stephan Dempe & Felix Harder & Patrick Mehlitz & Gerd Wachsmuth, 2019. "Solving inverse optimal control problems via value functions to global optimality," Journal of Global Optimization, Springer, vol. 74(2), pages 297-325, June.
    18. 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.
    19. 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.
    20. Nimrod Megiddo, 1981. "The Maximum Coverage Location Problem," Discussion Papers 490, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

    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:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0519-8. 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.