IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v111y2001i1d10.1023_a1017571214523.html
   My bibliography  Save this article

Contractibility of the Efficient Frontier of Three-Dimensional Simply-Shaded Sets

Author

Listed:
  • J. Benoist

    (University of Limoges)

  • N. Popovici

    (Babes-Bolyai University)

Abstract

The aim of this paper is to study the geometrical and topological structure of the efficient frontier of simply-shaded sets in a three-dimensional Euclidean space with respect to the usual positive cone. Our main result concerns the contractibility of the efficient frontier and refines a recent result of Daniilidis, Hadjisavvas, and Schaible (Ref. 1) regarding the connectedness of the efficient outcome set for three-criteria optimization problems involving continuous semistrictly quasiconcave objective functions.

Suggested Citation

  • J. Benoist & N. Popovici, 2001. "Contractibility of the Efficient Frontier of Three-Dimensional Simply-Shaded Sets," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 81-116, October.
  • Handle: RePEc:spr:joptap:v:111:y:2001:i:1:d:10.1023_a:1017571214523
    DOI: 10.1023/A:1017571214523
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1017571214523
    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:1017571214523?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. A. Daniilidis & N. Hadjisavvas & S. Schaible, 1997. "Connectedness of the Efficient Set for Three-Objective Quasiconcave Maximization Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 517-524, June.
    2. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
    3. J. Benoist, 1998. "Connectedness of the Efficient Set for Strictly Quasiconcave Sets," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 627-654, March.
    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. A. Daniilidis & Y. Garcia Ramos, 2007. "Some Remarks on the Class of Continuous (Semi-) Strictly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 37-48, April.
    2. N. Q. Huy & N. D. Yen, 2005. "Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 615-635, March.

    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. A. Daniilidis & N. Hadjisavvas, 1999. "Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 525-536, September.
    2. J. Benoist, 2001. "Contractibility of the Efficient Set in Strictly Quasiconcave Vector Maximization," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 325-336, August.
    3. J. Benoist, 1998. "Connectedness of the Efficient Set for Strictly Quasiconcave Sets," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 627-654, March.
    4. N. Q. Huy & N. D. Yen, 2005. "Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 615-635, March.
    5. S.T. Hackman & U. Passy, 2002. "Maximizing a Linear Fractional Function on a Pareto Efficient Frontier," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 83-103, April.
    6. E. K. Makarov & N. N. Rachkovski, 2001. "Efficient Sets of Convex Compacta are Arcwise Connected," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 159-172, July.
    7. Jean-Marc Bonnisseau & Lalaina Rakotonindrainy, 2017. "Existence of equilibrium in OLG economies with increasing returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 111-129, January.
    8. Tian, Guoqiang, 2004. "On the Informational Requirements of Decentralized Pareto-Satisfactory Mechanisms in Economies with Increasing Returns," MPRA Paper 41226, University Library of Munich, Germany, revised Oct 2006.
    9. Antoine Mandel, 2009. "Changes in the firms behavior after the opening of markets of allowances," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 1-25, July.
    10. Riccardo Cambini & Laura Carosi & Laura Martein, 2017. "Generating the efficient frontier of a class of bicriteria generalized fractional programming," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 81-101, November.
    11. Bonnisseau, Jean-Marc & Medecin, Jean-Philippe, 2001. "Existence of marginal pricing equilibria in economies with externalities and non-convexities," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 271-294, December.
    12. Bonnisseau, J.-M. & Cornet, B., 2008. "Existence of equilibria with a tight marginal pricing rule," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 613-624, July.
    13. Brown, Donald J. & Heller, Walter P. & Starr, Ross M., 1992. "Two-part marginal cost pricing equilibria: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 57(1), pages 52-72.
    14. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    15. Dehez, Pierre & Dreze, Jacques H. & Suzuki, Takashi, 2003. "Imperfect competition a la Negishi, also with fixed costs," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 219-237, June.
    16. J. M. Bonnisseau & A. Jamin, 2008. "Equilibria with Increasing Returns: Sufficient Conditions on Bounded Production Allocations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1033-1068, December.
    17. Jorge Rivera, 2004. "Una aplicación del análisis no diferenciable a la economía matemática: caracterización de la hipótesis de libre eliminación por medio del cono normal a la frontera del conjunto," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 19(2), pages 147-156, December.
    18. Bonnisseau, Jean-Marc & Meddeb, Moncef, 1999. "Existence of equilibria in economies with increasing returns and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 287-307, April.
    19. Tian, Guoqiang, 2009. "Implementation in economies with non-convex production technologies unknown to the designer," Games and Economic Behavior, Elsevier, vol. 66(1), pages 526-545, May.
    20. Berliant, M. & Ten Raa, T., 2003. "Increasing returns to scale and perfect competition : The role of land," Other publications TiSEM c4f1929e-6651-4959-b757-4, Tilburg University, School of Economics and Management.

    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:111:y:2001:i:1:d:10.1023_a:1017571214523. 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.