IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v141y2009i1d10.1007_s10957-008-9485-0.html
   My bibliography  Save this article

Existence of Solutions of a Vector Optimization Problem with a Generic Lower Semicontinuous Objective Function

Author

Listed:
  • A. J. Zaslavski

    (Technion)

Abstract

We study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of lower semicontinuous bounded-from-below objective functions $\mathcal{A}$ . We establish the existence of a G δ everywhere dense subset ℱ of $\mathcal{A}$ such that, for any objective function belonging to ℱ, the corresponding minimization problem possesses a solution.

Suggested Citation

  • A. J. Zaslavski, 2009. "Existence of Solutions of a Vector Optimization Problem with a Generic Lower Semicontinuous Objective Function," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 217-230, April.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:1:d:10.1007_s10957-008-9485-0
    DOI: 10.1007/s10957-008-9485-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9485-0
    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/s10957-008-9485-0?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. A. J. Zaslavski, 2008. "Generic Existence of Solutions in Vector Optimization on Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 139-153, January.
    2. Mario Villalobos-Arias & Carlos Coello & Onésimo Hernández-Lerma, 2006. "Asymptotic convergence of a simulated annealing algorithm for multiobjective optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 353-362, October.
    3. T. Q. Bao & P. Gupta & B. S. Mordukhovich, 2007. "Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 179-203, November.
    Full references (including those not matched with items on IDEAS)

    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. M. Durea & R. Strugariu, 2011. "On parametric vector optimization via metric regularity of constraint systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 409-425, December.
    2. Boris S. Mordukhovich & Nguyen Mau Nam & Hung M. Phan, 2012. "Variational Analysis of Marginal Functions with Applications to Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 557-586, March.
    3. L. Q. Anh & P. Q. Khanh & D. T. M. Van, 2012. "Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 42-59, April.
    4. Hélène Le Cadre & Mustapha Bouhtou & Bruno Tuffin, 2009. "Consumers’ preference modeling to price bundle offers in the telecommunications industry: a game with competition among operators," Netnomics, Springer, vol. 10(2), pages 171-208, October.
    5. P. Khanh & L. Tung, 2015. "First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 419-440, July.
    6. N. Gadhi & S. Dempe, 2012. "Necessary Optimality Conditions and a New Approach to Multiobjective Bilevel Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 100-114, October.
    7. Gianfranco Chicco & Andrea Mazza, 2020. "Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the ‘Rush to Heuristics’," Energies, MDPI, vol. 13(19), pages 1-38, September.
    8. Maria Rossana D. de Veluz & Anak Agung Ngurah Perwira Redi & Renato R. Maaliw & Satria Fadil Persada & Yogi Tri Prasetyo & Michael Nayat Young, 2023. "Scenario-Based Multi-Objective Location-Routing Model for Pre-Disaster Planning: A Philippine Case Study," Sustainability, MDPI, vol. 15(6), pages 1-33, March.
    9. Sayantan Mitra & Sriparna Saha, 2019. "A multiobjective multi-view cluster ensemble technique: Application in patient subclassification," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-30, May.
    10. Thai Doan Chuong & Do Sang Kim, 2016. "A class of nonsmooth fractional multiobjective optimization problems," Annals of Operations Research, Springer, vol. 244(2), pages 367-383, September.
    11. Nguyen Quang Huy & Do Sang Kim & Nguyen Van Tuyen, 2017. "Existence Theorems in Vector Optimization with Generalized Order," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 728-745, September.
    12. Jane J. Ye, 2011. "Necessary Optimality Conditions for Multiobjective Bilevel Programs," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 165-184, February.
    13. Aram V. Arutyunov & Boris S. Mordukhovich & Sergey E. Zhukovskiy, 2023. "Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 177-198, January.
    14. Vo Duc Thinh & Thai Doan Chuong, 2018. "Directionally generalized differentiation for multifunctions and applications to set-valued programming problems," Annals of Operations Research, Springer, vol. 269(1), pages 727-751, October.
    15. Thai Doan Chuong, 2020. "Optimality conditions for nonsmooth multiobjective bilevel optimization problems," Annals of Operations Research, Springer, vol. 287(2), pages 617-642, 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:141:y:2009:i:1:d:10.1007_s10957-008-9485-0. 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.