IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v174y2017i3d10.1007_s10957-017-1146-8.html
   My bibliography  Save this article

Existence Theorems in Vector Optimization with Generalized Order

Author

Listed:
  • Nguyen Quang Huy

    (Hanoi Pedagogical University 2)

  • Do Sang Kim

    (Pukyong National University)

  • Nguyen Van Tuyen

    (Hanoi Pedagogical University 2)

Abstract

In the present paper, we establish some results for the existence of optimal solutions in vector optimization in infinite-dimensional spaces, where the optimality notion is understood in the sense of generalized order (may not be convex and/or conical). This notion is induced by the concept of set extremality and covers many of the conventional notions of optimality in vector optimization. Some sufficient optimality conditions for optimal solutions of a class of vector optimization problems, which satisfies the free disposal hypothesis, are also examined.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1146-8
    DOI: 10.1007/s10957-017-1146-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1146-8
    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/s10957-017-1146-8?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. Jonathan M. Borwein, 1983. "On the Existence of Pareto Efficient Points," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 64-73, February.
    2. Jean-Marc Bonnisseau & Bertrand Crettez, 2007. "On the Characterization of Efficient Production Vectors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 213-223, May.
    3. Y. Sonntag & C. Zalinescu, 2000. "Comparison of Existence Results for Efficient Points," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 161-188, April.
    4. Dinh The Luc, 1989. "An Existence Theorem in Vector Optimization," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 693-699, November.
    5. 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.
    6. Pirro Oppezzi & Anna Rossi, 2015. "Improvement Sets and Convergence of Optimal Points," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 405-419, May.
    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. Nergiz Kasimbeyli, 2015. "Existence and characterization theorems in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 62(1), pages 155-165, May.
    2. K.F. Ng & X.Y. Zheng, 2002. "Existence of Efficient Points in Vector Optimization and Generalized Bishop–Phelps Theorem," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 29-47, October.
    3. Y. Sonntag & C. Zalinescu, 2000. "Comparison of Existence Results for Efficient Points," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 161-188, April.
    4. 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.
    5. Feng Guo & Liguo Jiao, 2023. "A new scheme for approximating the weakly efficient solution set of vector rational optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 905-930, August.
    6. 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.
    7. 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.
    8. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    9. J. Jahn & A. A. Khan & P. Zeilinger, 2005. "Second-Order Optimality Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 331-347, May.
    10. A. Engau & M. M. Wiecek, 2007. "Cone Characterizations of Approximate Solutions in Real Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 499-513, September.
    11. Li-Wen Zhou & Nan-Jing Huang, 2013. "Existence of Solutions for Vector Optimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 44-53, April.
    12. Fabián Flores-Bazán & Sigifredo Laengle & Gino Loyola, 2013. "Characterizing the efficient points without closedness or free-disposability," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(2), pages 401-410, March.
    13. 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.
    14. Yarui Duan & Liguo Jiao & Pengcheng Wu & Yuying Zhou, 2022. "Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 148-171, October.
    15. X. Y. Zheng & X. M. Yang & K. L. Teo, 2007. "Some Geometrical Aspects of Efficient Points in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 275-288, May.
    16. Juan Aparicio & Fernando Borras & Jesus T. Pastor & Jose L. Zofio, 2016. "Loss Distance Functions and Profit Function: General Duality Results," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor (ed.), Advances in Efficiency and Productivity, chapter 0, pages 71-96, Springer.
    17. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    18. Jayswal, Anurag & Singh, Shipra & Kurdi, Alia, 2016. "Multitime multiobjective variational problems and vector variational-like inequalities," European Journal of Operational Research, Elsevier, vol. 254(3), pages 739-745.
    19. 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.
    20. Harold Benson, 2012. "An outcome space algorithm for optimization over the weakly efficient set of a multiple objective nonlinear programming problem," Journal of Global Optimization, Springer, vol. 52(3), pages 553-574, March.

    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:174:y:2017:i:3:d:10.1007_s10957-017-1146-8. 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.