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A subgradient method for multiobjective optimization

Author

Listed:
  • J. Cruz Neto
  • G. Silva
  • O. Ferreira
  • J. Lopes

Abstract

A method for solving quasiconvex nondifferentiable unconstrained multiobjective optimization problems is proposed in this paper. This method extends to the multiobjective case of the classical subgradient method for real-valued minimization. Assuming the basically componentwise quasiconvexity of the objective components, full convergence (to Pareto optimal points) of all the sequences produced by the method is established. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • J. Cruz Neto & G. Silva & O. Ferreira & J. Lopes, 2013. "A subgradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 461-472, April.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:3:p:461-472
    DOI: 10.1007/s10589-012-9494-7
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Hiroki Tanabe & Ellen H. Fukuda & Nobuo Yamashita, 2019. "Proximal gradient methods for multiobjective optimization and their applications," Computational Optimization and Applications, Springer, vol. 72(2), pages 339-361, March.
    2. Fabrice Poirion & Quentin Mercier & Jean-Antoine Désidéri, 2017. "Descent algorithm for nonsmooth stochastic multiobjective optimization," Computational Optimization and Applications, Springer, vol. 68(2), pages 317-331, November.
    3. G. Bento & J. Cruz Neto & G. López & Antoine Soubeyran & J. Souza, 2018. "The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem," Post-Print hal-01985333, HAL.
    4. N. Hoseini Monjezi & S. Nobakhtian, 2022. "An inexact multiple proximal bundle algorithm for nonsmooth nonconvex multiobjective optimization problems," Annals of Operations Research, Springer, vol. 311(2), pages 1123-1154, April.
    5. Mike G. Tsionas, 2021. "Multi-criteria optimization in regression," Annals of Operations Research, Springer, vol. 306(1), pages 7-25, November.
    6. F. Lara, 2022. "On Strongly Quasiconvex Functions: Existence Results and Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 891-911, March.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Chen, Wang & Yang, Xinmin & Zhao, Yong, 2023. "Memory gradient method for multiobjective optimization," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    12. Felipe Lara & Alireza Kabgani, 2021. "On global subdifferentials with applications in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 81(4), pages 881-900, December.
    13. Tsionas, Mike G., 2018. "A Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms," Omega, Elsevier, vol. 77(C), pages 73-79.
    14. Bennet Gebken & Sebastian Peitz, 2021. "An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 696-723, March.
    15. 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.
    16. 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.
    17. Xiaopeng Zhao & Markus A. Köbis & Yonghong Yao & Jen-Chih Yao, 2021. "A Projected Subgradient Method for Nondifferentiable Quasiconvex Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 82-107, July.
    18. 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.

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