IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v203y2024i1d10.1007_s10957-024-02535-x.html
   My bibliography  Save this article

On the Extension of Dai-Liao Conjugate Gradient Method for Vector Optimization

Author

Listed:
  • Qingjie Hu

    (Guilin University of Electronic Technology
    Center for Applied Mathematics of Guangxi (GUET)
    Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation)

  • Ruyun Li

    (Guilin University of Electronic Technology
    Center for Applied Mathematics of Guangxi (GUET)
    Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation)

  • Yanyan Zhang

    (Guilin University of Electronic Technology
    Center for Applied Mathematics of Guangxi (GUET)
    Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation)

  • Zhibin Zhu

    (Guilin University of Electronic Technology
    Center for Applied Mathematics of Guangxi (GUET)
    Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation)

Abstract

In this paper, we extend the Dai-Liao conjugate gradient method to vector optimization. Firstly, we analyze the global convergence of the direct extension version of the Dai-Liao conjugate gradient method for K-strongly convex vector functions. Secondly, we investigate the global convergence of the vector version of restricted non-negative Dai-Liao conjugate gradient method for general vector functions. Additionally, we discuss the global convergence of the vector version of modified Dai-Liao conjugate gradient method for general vector functions. Finally, numerical experiments demonstrate that the proposed conjugate gradient methods are effective for solving vector optimization problems. In particular, these methods can effectively generate the Pareto frontiers for the test problems.

Suggested Citation

  • Qingjie Hu & Ruyun Li & Yanyan Zhang & Zhibin Zhu, 2024. "On the Extension of Dai-Liao Conjugate Gradient Method for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 810-843, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02535-x
    DOI: 10.1007/s10957-024-02535-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02535-x
    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/s10957-024-02535-x?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. Miglierina, E. & Molho, E. & Recchioni, M.C., 2008. "Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 662-682, August.
    2. Gravel, Marc & Martel, Jean Marc & Nadeau, Raymond & Price, Wilson & Tremblay, Richard, 1992. "A multicriterion view of optimal resource allocation in job-shop production," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 230-244, August.
    3. Villacorta, Kely D.V. & Oliveira, P. Roberto, 2011. "An interior proximal method in vector optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 485-492, November.
    4. Johannes Jahn & Andreas Kirsch & Carmen Wagner, 2004. "Optimization of rod antennas of mobile phones," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 37-51, February.
    5. Leschine, Thomas M. & Wallenius, Hannele & Verdini, William A., 1992. "Interactive multiobjective analysis and assimilative capacity-based ocean disposal decisions," European Journal of Operational Research, Elsevier, vol. 56(2), pages 278-289, January.
    6. M. L. N. Gonçalves & L. F. Prudente, 2020. "On the extension of the Hager–Zhang conjugate gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 889-916, July.
    7. Wang Chen & Xinmin Yang & Yong Zhao, 2023. "Conditional gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 857-896, July.
    8. Thai Chuong, 2013. "Newton-like methods for efficient solutions in vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 495-516, April.
    9. Qing-Rui He & Chun-Rong Chen & Sheng-Jie Li, 2023. "Spectral conjugate gradient methods for vector optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 457-489, 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. Qing-Rui He & Sheng-Jie Li & Bo-Ya Zhang & Chun-Rong Chen, 2024. "A family of conjugate gradient methods with guaranteed positiveness and descent for vector optimization," Computational Optimization and Applications, Springer, vol. 89(3), pages 805-842, December.
    2. Jiawei Chen & Yushan Bai & Guolin Yu & Xiaoqing Ou & Xiaolong Qin, 2025. "A PRP Type Conjugate Gradient Method Without Truncation for Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-30, January.
    3. Gonçalves, M.L.N. & Lima, F.S. & Prudente, L.F., 2022. "A study of Liu-Storey conjugate gradient methods for vector optimization," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Wang Chen & Xinmin Yang & Yong Zhao, 2023. "Conditional gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 857-896, July.
    5. Qing-Rui He & Chun-Rong Chen & Sheng-Jie Li, 2023. "Spectral conjugate gradient methods for vector optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 457-489, November.
    6. M. L. N. Gonçalves & L. F. Prudente, 2020. "On the extension of the Hager–Zhang conjugate gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 889-916, July.
    7. Ellen H. Fukuda & L. M. Graña Drummond & Fernanda M. P. Raupp, 2016. "An external penalty-type method for multicriteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 493-513, July.
    8. Bento, G.C. & Cruz Neto, J.X. & Oliveira, P.R. & Soubeyran, A., 2014. "The self regulation problem as an inexact steepest descent method for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 235(3), pages 494-502.
    9. G. Cocchi & M. Lapucci, 2020. "An augmented Lagrangian algorithm for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 29-56, September.
    10. Harold P. Benson & Serpil Sayin, 1997. "Towards finding global representations of the efficient set in multiple objective mathematical programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 47-67, February.
    11. N. Mahdavi-Amiri & F. Salehi Sadaghiani, 2017. "Strictly feasible solutions and strict complementarity in multiple objective linear optimization," 4OR, Springer, vol. 15(3), pages 303-326, September.
    12. G. Tohidi & H. Hassasi, 2018. "Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(3), pages 203-217, April.
    13. L. F. Prudente & D. R. Souza, 2022. "A Quasi-Newton Method with Wolfe Line Searches for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1107-1140, September.
    14. Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
    15. Hokkanen, Joonas & Salminen, Pekka, 1997. "Choosing a solid waste management system using multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 98(1), pages 19-36, April.
    16. Nowak, Maciej, 2004. "Preference and veto thresholds in multicriteria analysis based on stochastic dominance," European Journal of Operational Research, Elsevier, vol. 158(2), pages 339-350, October.
    17. M. L. N. Gonçalves & F. S. Lima & L. F. Prudente, 2022. "Globally convergent Newton-type methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 83(2), pages 403-434, November.
    18. Ernesto G. Birgin, 2020. "Preface of the special issue dedicated to the XII Brazilian workshop on continuous optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 615-619, July.
    19. Recchioni, Maria Cristina & Tedeschi, Gabriele, 2017. "From bond yield to macroeconomic instability: A parsimonious affine model," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1116-1135.
    20. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, 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:203:y:2024:i:1:d:10.1007_s10957-024-02535-x. 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.