IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v263y2017i2p356-366.html
   My bibliography  Save this article

Nonmonotone gradient methods for vector optimization with a portfolio optimization application

Author

Listed:
  • Qu, Shaojian
  • Ji, Ying
  • Jiang, Jianlin
  • Zhang, Qingpu

Abstract

This paper proposes two nonmonotone gradient algorithms for a class of vector optimization problems with a C−convex objective function. We establish both the global and local convergence results for the new algorithms. We then apply the new algorithms to a portfolio optimization problem under multi-criteria considerations.

Suggested Citation

  • Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.
    • Handle: RePEc:eee:ejores:v:263:y:2017:i:2:p:356-366
    DOI: 10.1016/j.ejor.2017.05.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717304551
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.05.027?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. Y. H. Dai, 2002. "On the Nonmonotone Line Search," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 315-330, February.
    2. Shao-Jian Qu & Mark Goh & Robert Souza & Tie-Nan Wang, 2014. "Proximal Point Algorithms for Convex Multi-criteria Optimization with Applications to Supply Chain Risk Management," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 949-956, December.
    3. Ellen Fukuda & L. Graña Drummond, 2013. "Inexact projected gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 473-493, April.
    4. Shao-Jian Qu & Mark Goh & Xiujie Zhang, 2011. "A new hybrid method for nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 49(3), pages 493-520, July.
    5. Qu, Shaojian & Liu, Chen & Goh, Mark & Li, Yijun & Ji, Ying, 2014. "Nonsmooth multiobjective programming with quasi-Newton methods," European Journal of Operational Research, Elsevier, vol. 235(3), pages 503-510.
    6. Alfredo N. Iusem & B. F. Svaiter & Marc Teboulle, 1994. "Entropy-Like Proximal Methods in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 790-814, November.
    7. Glaydston Carvalho Bento & J.X. Cruz Neto & Antoine Soubeyran, 2014. "A Proximal Point-Type Method for Multicriteria Optimization," Post-Print hal-01463765, HAL.
    8. Shi, Zhenjun & Wang, Shengquan, 2011. "Nonmonotone adaptive trust region method," European Journal of Operational Research, Elsevier, vol. 208(1), pages 28-36, January.
    9. Brito, A.S. & Cruz Neto, J.X. & Santos, P.S.M. & Souza, S.S., 2017. "A relaxed projection method for solving multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 256(1), pages 17-23.
    10. 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.
    11. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
    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. Wu, Zili, 2018. "Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping," European Journal of Operational Research, Elsevier, vol. 265(2), pages 448-453.
    2. 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.
    3. Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
    4. Chen, Jian & Tang, Liping & Yang, Xinmin, 2023. "A Barzilai-Borwein descent method for multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 196-209.
    5. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
    6. Kanako Mita & Ellen H. Fukuda & Nobuo Yamashita, 2019. "Nonmonotone line searches for unconstrained multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 63-90, September.

    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. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.
    2. 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).
    3. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
    4. 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.
    5. 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.
    6. 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.
    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. Brito, A.S. & Cruz Neto, J.X. & Santos, P.S.M. & Souza, S.S., 2017. "A relaxed projection method for solving multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 256(1), pages 17-23.
    9. 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.
    10. 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.
    11. J. Y. Bello Cruz & G. Bouza Allende, 2014. "A Steepest Descent-Like Method for Variable Order Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 371-391, August.
    12. X. M. Wang & J. H. Wang & C. Li, 2023. "Convergence of Inexact Steepest Descent Algorithm for Multiobjective Optimizations on Riemannian Manifolds Without Curvature Constraints," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 187-214, July.
    13. P. B. Assunção & O. P. Ferreira & L. F. Prudente, 2021. "Conditional gradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 78(3), pages 741-768, April.
    14. 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.
    15. H. Apolinário & E. Papa Quiroz & P. Oliveira, 2016. "A scalarization proximal point method for quasiconvex multiobjective minimization," Journal of Global Optimization, Springer, vol. 64(1), pages 79-96, January.
    16. Alfredo N. Iusem & Jefferson G. Melo & Ray G. Serra, 2021. "A Strongly Convergent Proximal Point Method for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 183-200, July.
    17. Rocha, Rogério Azevedo & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros & Souza, Michael, 2016. "Logarithmic quasi-distance proximal point scalarization method for multi-objective programming," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 856-867.
    18. Kabgani, Alireza & Soleimani-damaneh, Majid, 2022. "Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 35-45.
    19. Rogério A. Rocha & Paulo R. Oliveira & Ronaldo M. Gregório & Michael Souza, 2016. "A Proximal Point Algorithm with Quasi-distance in Multi-objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 964-979, December.
    20. Vieira, D.A.G. & Lisboa, A.C., 2019. "A cutting-plane method to nonsmooth multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 822-829.

    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:eee:ejores:v:263:y:2017:i:2:p:356-366. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.