IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v184y2020i2d10.1007_s10957-019-01608-6.html
   My bibliography  Save this article

On the Structure of the Weakly Efficient Set for Quasiconvex Vector Minimization

Author

Listed:
  • Frank Plastria

    (Prof. Em. BUTO, Vrije Universiteit Brussel)

Abstract

We investigate conditions under which the weakly efficient set for minimization of m objective functions on a closed and convex $$X\subset \mathbb R^d$$X⊂Rd ($$m>d$$m>d) is fully determined by the weakly efficient sets for all n-objective subsets for some $$n

Suggested Citation

  • Frank Plastria, 2020. "On the Structure of the Weakly Efficient Set for Quasiconvex Vector Minimization," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 547-564, February.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01608-6
    DOI: 10.1007/s10957-019-01608-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01608-6
    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/s10957-019-01608-6?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. B. Martos, 1965. "The Direct Power of Adjacent Vertex Programming Methods," Management Science, INFORMS, vol. 12(3), pages 241-252, November.
    2. Suliman Al-Homidan & Nicolas Hadjisavvas & Loai Shaalan, 2018. "Transformation of Quasiconvex Functions to Eliminate Local Minima," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 93-105, April.
    3. Plastria, F., 1984. "Localization in single facility location," European Journal of Operational Research, Elsevier, vol. 18(2), pages 215-219, November.
    4. A.M. Rodríguez-Chía & J. Puerto, 2002. "Geometrical Description of the Weakly Efficient Solution Set for Multicriteria Location Problems," Annals of Operations Research, Springer, vol. 111(1), pages 181-196, March.
    5. James Ward, 1989. "Structure of Efficient Sets for Convex Objectives," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 249-257, May.
    6. Diewert, W. E. & Avriel, M. & Zang, I., 1981. "Nine kinds of quasiconcavity and concavity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 397-420, December.
    7. F. Flores-Bazán & C. Vera, 2006. "Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 185-207, August.
    8. Matthias Ehrgott & Stefan Nickel, 2002. "On the number of criteria needed to decide Pareto optimality," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 329-345, June.
    9. Matthias Ehrgott & Stefan Nickel, 2002. "On the number of criteria needed to decide Pareto optimality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 329-345, June.
    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. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.

    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. Alzorba, Shaghaf & Günther, Christian & Popovici, Nicolae & Tammer, Christiane, 2017. "A new algorithm for solving planar multiobjective location problems involving the Manhattan norm," European Journal of Operational Research, Elsevier, vol. 258(1), pages 35-46.
    2. Melissa Gardenghi & Trinidad Gómez & Francisca Miguel & Margaret M. Wiecek, 2011. "Algebra of Efficient Sets for Multiobjective Complex Systems," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 385-410, May.
    3. Naoki Hamada & Shunsuke Ichiki, 2022. "Free Disposal Hull Condition to Verify When Efficiency Coincides with Weak Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 248-270, January.
    4. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    5. Lindroth, Peter & Patriksson, Michael & Strömberg, Ann-Brith, 2010. "Approximating the Pareto optimal set using a reduced set of objective functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1519-1534, December.
    6. Engau, Alexander, 2009. "Tradeoff-based decomposition and decision-making in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 199(3), pages 883-891, December.
    7. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    8. S. Selcuk Erenguc, 1988. "Multiproduct dynamic lot‐sizing model with coordinated replenishments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 1-22, February.
    9. Blackorby, Charles & Brett, Craig, 2004. "Capital Taxation In A Simple Finite-Horizon Olg Model," The Warwick Economics Research Paper Series (TWERPS) 709, University of Warwick, Department of Economics.
    10. Emilio Priego & Francisco Fernández García, 1993. "A polygonal upper bound for the efficient set for single-facility location problems with mixed norms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 107-116, December.
    11. Carrizosa, Emilio & Rodriguez-Chia, Antonio M., 1997. "Weber problems with alternative transportation systems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 87-93, February.
    12. Ovidiu Bagdasar & Nicolae Popovici, 2018. "Unifying local–global type properties in vector optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 155-179, October.
    13. Sadorsky, P. A., 1989. "Measuring Resource Scarcity in Non-renewable Resources with Inequality Constrained Estimation," Queen's Institute for Economic Research Discussion Papers 275216, Queen's University - Department of Economics.
    14. Sorin-Mihai Grad & Felipe Lara, 2022. "An extension of the proximal point algorithm beyond convexity," Journal of Global Optimization, Springer, vol. 82(2), pages 313-329, February.
    15. A. Kabgani & F. Lara, 2023. "Semistrictly and neatly quasiconvex programming using lower global subdifferentials," Journal of Global Optimization, Springer, vol. 86(4), pages 845-865, August.
    16. Blackorby, Charles & Murty, Sushama, 2007. "Unit versus ad valorem taxes: Monopoly in general equilibrium," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 817-822, April.
    17. Blackorby, Charles & Brett, Craig, 2000. "Fiscal Federalism Revisited," Journal of Economic Theory, Elsevier, vol. 92(2), pages 300-317, June.
    18. Hefti, Andreas, 2016. "On the relationship between uniqueness and stability in sum-aggregative, symmetric and general differentiable games," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 83-96.
    19. Nguyen Xuan Hai & Nguyen Hong Quan & Vo Viet Tri, 2023. "Some saddle-point theorems for vector-valued functions," Journal of Global Optimization, Springer, vol. 86(1), pages 141-161, May.
    20. Denizel, Meltem & Erenguc, Selcuk & Benson, Harold P., 1997. "Dynamic lot-sizing with setup cost reduction," European Journal of Operational Research, Elsevier, vol. 100(3), pages 537-549, 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:184:y:2020:i:2:d:10.1007_s10957-019-01608-6. 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.