IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v154y2012i2d10.1007_s10957-012-0007-8.html
   My bibliography  Save this article

Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems

Author

Listed:
  • Haijun Liu

    (Inner Mongolia Agricultural University
    Inner Mongolia University)

  • Neng Fan

    (Sandia National Laboratories)

  • Panos M. Pardalos

    (University of Florida
    National Research University, Higher School of Economics)

Abstract

By constructing a kind of generalized Lagrange function for a class of multiobjective fractional optimal control problems, sufficient and necessary conditions for existence of generalized weak saddle points are established. In addition, the relationship between weak efficiency and generalized weak saddle points is discussed.

Suggested Citation

  • Haijun Liu & Neng Fan & Panos M. Pardalos, 2012. "Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 370-381, August.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-012-0007-8
    DOI: 10.1007/s10957-012-0007-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0007-8
    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/s10957-012-0007-8?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. L. Grosset & B. Viscolani, 2006. "Reciprocal Optimal Control Problems and the Associated Pareto Frontier," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 113-123, July.
    2. D. S. Kim & S. J. Kim & M. H. Kim, 2006. "Optimality and Duality for a Class of Nondifferentiable Multiobjective Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 131-146, April.
    3. G. Wanka, 2000. "Multiobjective Control Approximation Problems: Duality and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 457-475, May.
    4. Z. A. Liang & H. X. Huang & P. M. Pardalos, 2001. "Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 611-619, September.
    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. X. J. Long, 2011. "Optimality Conditions and Duality for Nondifferentiable Multiobjective Fractional Programming Problems with (C,α,ρ,d)-convexity," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 197-208, January.
    2. Xiaojun Lei & Zhian Liang, 2008. "Study on the Duality between MFP and ACP," Modern Applied Science, Canadian Center of Science and Education, vol. 2(6), pages 1-81, November.
    3. Khoirunnisa Rohadatul Aisy Muslihin & Endang Rusyaman & Diah Chaerani, 2022. "Conic Duality for Multi-Objective Robust Optimization Problem," Mathematics, MDPI, vol. 10(21), pages 1-22, October.
    4. I. Ahmad & Z. Husain, 2006. "Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 255-275, May.
    5. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    6. V. Jeyakumar & G. Y. Li, 2011. "Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 292-303, November.
    7. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
    8. I. Ahmad & Z. Husain & S. Sharma, 2009. "Higher-Order Duality in Nondifferentiable Minimax Programming with Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 1-12, April.
    9. Jeyakumar, V. & Li, G.Y. & Srisatkunarajah, S., 2013. "Strong duality for robust minimax fractional programming problems," European Journal of Operational Research, Elsevier, vol. 228(2), pages 331-336.
    10. Ahmad, I. & Sharma, Sarita, 2008. "Symmetric duality for multiobjective fractional variational problems involving cones," European Journal of Operational Research, Elsevier, vol. 188(3), pages 695-704, August.
    11. Hong Yang & Angang Cui, 2023. "The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with ( B K ,ρ )−Invexity," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    12. Arun Kumar Tripathy, 2021. "The Study Higher-order Wolfe-type Non-differentiable Multiple Objective Symmetric Duality Involving Generalized Convex Functions," SN Operations Research Forum, Springer, vol. 2(4), pages 1-18, December.
    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. D. S. Kim & S. J. Kim & M. H. Kim, 2006. "Optimality and Duality for a Class of Nondifferentiable Multiobjective Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 131-146, April.
    15. Arshpreet Kaur & Mahesh K Sharma, 2022. "Correspondence between a new class of generalized cone convexity and higher order duality," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 550-560, June.
    16. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.
    17. Abderrahman Bouhamidi & Mohammed Bellalij & Rentsen Enkhbat & Khalid Jbilou & Marcos Raydan, 2018. "Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 163-177, January.
    18. Washington Alves Oliveira & Marko Antonio Rojas-Medar & Antonio Beato-Moreno & Maria Beatriz Hernández-Jiménez, 2019. "Necessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems," Journal of Global Optimization, Springer, vol. 74(2), pages 233-253, June.
    19. Anurag Jayswal & Vivek Singh & Krishna Kummari, 2017. "Duality for nondifferentiable minimax fractional programming problem involving higher order $$(\varvec{C},\varvec{\alpha}, \varvec{\rho}, \varvec{d})$$ ( C , α , ρ , d ) -convexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 598-617, September.
    20. Altannar Chinchuluun & Dehui Yuan & Panos Pardalos, 2007. "Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity," Annals of Operations Research, Springer, vol. 154(1), pages 133-147, October.

    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:154:y:2012:i:2:d:10.1007_s10957-012-0007-8. 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.