IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v72y2018i2d10.1007_s10898-018-0627-0.html
   My bibliography  Save this article

A vector linear programming approach for certain global optimization problems

Author

Listed:
  • Daniel Ciripoi

    (Friedrich Schiller University Jena)

  • Andreas Löhne

    (Friedrich Schiller University Jena)

  • Benjamin Weißing

    (Friedrich Schiller University Jena)

Abstract

Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple objective linear programs (MOLP). The modification of the MOLP algorithms results in a more efficient treatment of the studied optimization problems. This paper generalizes results of Schulz and Mittal (Math Program 141(1–2):103–120, 2013) on quasi-concave problems and Shao and Ehrgott (Optimization 65(2):415–431, 2016) on multiplicative linear programs. Furthermore, it improves results of Löhne and Wagner (J Glob Optim 69(2):369–385, 2017) on minimizing the difference $$f=g-h$$ f = g - h of two convex functions g, h where either g or h is polyhedral. Numerical examples are given and the results are compared with the global optimization software BARON.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:2:d:10.1007_s10898-018-0627-0
    DOI: 10.1007/s10898-018-0627-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-018-0627-0
    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/s10898-018-0627-0?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. 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.
    2. Albert Ferrer & Adil Bagirov & Gleb Beliakov, 2015. "Solving DC programs using the cutting angle method," Journal of Global Optimization, Springer, vol. 61(1), pages 71-89, January.
    3. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, vol. 59(4), pages 811-836, August.
    4. Matthias Ehrgott & Andreas Löhne & Lizhen Shao, 2012. "A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming," Journal of Global Optimization, Springer, vol. 52(4), pages 757-778, April.
    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. Gabriela Kov'av{c}ov'a & Birgit Rudloff, 2018. "Time consistency of the mean-risk problem," Papers 1806.10981, arXiv.org, revised Jan 2020.
    2. Daniel Dörfler, 2022. "On the Approximation of Unbounded Convex Sets by Polyhedra," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 265-287, July.
    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.

    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. Zachary Feinstein & Birgit Rudloff, 2017. "A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle," Journal of Global Optimization, Springer, vol. 68(1), pages 47-69, May.
    2. Zachary Feinstein & Birgit Rudloff, 2015. "A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle," Papers 1508.02367, arXiv.org, revised Jul 2016.
    3. Bazovkin, Pavel, 2014. "Geometrical framework for robust portfolio optimization," Discussion Papers in Econometrics and Statistics 01/14, University of Cologne, Institute of Econometrics and Statistics.
    4. Nghe, Philippe & Mulder, Bela M. & Tans, Sander J., 2018. "A graph-based algorithm for the multi-objective optimization of gene regulatory networks," European Journal of Operational Research, Elsevier, vol. 270(2), pages 784-793.
    5. Fritz Bökler & Sophie N. Parragh & Markus Sinnl & Fabien Tricoire, 2024. "An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 263-290, August.
    6. Löhne, Andreas & Weißing, Benjamin, 2017. "The vector linear program solver Bensolve – notes on theoretical background," European Journal of Operational Research, Elsevier, vol. 260(3), pages 807-813.
    7. 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.
    8. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.
    9. Britta Schulze & Kathrin Klamroth & Michael Stiglmayr, 2019. "Multi-objective unconstrained combinatorial optimization: a polynomial bound on the number of extreme supported solutions," Journal of Global Optimization, Springer, vol. 74(3), pages 495-522, July.
    10. Zachary Feinstein & Birgit Rudloff, 2021. "Characterizing and Computing the Set of Nash Equilibria via Vector Optimization," Papers 2109.14932, arXiv.org, revised Dec 2022.
    11. Pascal Halffmann & Tobias Dietz & Anthony Przybylski & Stefan Ruzika, 2020. "An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem," Journal of Global Optimization, Springer, vol. 77(4), pages 715-742, August.
    12. Kellner, Florian & Lienland, Bernhard & Utz, Sebastian, 2019. "An a posteriori decision support methodology for solving the multi-criteria supplier selection problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 505-522.
    13. c{C}au{g}{i}n Ararat & Nurtai Meimanjan, 2019. "Computation of systemic risk measures: a mixed-integer programming approach," Papers 1903.08367, arXiv.org, revised Aug 2023.
    14. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "A Semidefinite Programming approach for solving Multiobjective Linear Programming," Journal of Global Optimization, Springer, vol. 58(3), pages 465-480, March.
    15. 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.
    16. Yldenilson Torres Almeida & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos de Oliveira Souza, 2020. "A modified proximal point method for DC functions on Hadamard manifolds," Computational Optimization and Applications, Springer, vol. 76(3), pages 649-673, July.
    17. 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.
    18. Julius Bauß & Michael Stiglmayr, 2024. "Augmenting bi-objective branch and bound by scalarization-based information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 85-121, August.
    19. László Csirmaz, 2016. "Using multiobjective optimization to map the entropy region," Computational Optimization and Applications, Springer, vol. 63(1), pages 45-67, January.
    20. Soghra Nobakhtian & Narjes Shafiei, 2017. "A Benson type algorithm for nonconvex multiobjective programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 271-287, July.

    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:72:y:2018:i:2:d:10.1007_s10898-018-0627-0. 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.