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Nonsmooth multiobjective programming with quasi-Newton methods

Author

Listed:
  • Qu, Shaojian
  • Liu, Chen
  • Goh, Mark
  • Li, Yijun
  • Ji, Ying

Abstract

This paper proposes a new algorithm to solve nonsmooth multiobjective programming. The algorithm is a descent direction method to obtain the critical point (a necessary condition for Pareto optimality). We analyze both global and local convergence results under some assumptions. Numerical tests are also given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:3:p:503-510
    DOI: 10.1016/j.ejor.2014.01.022
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    References listed on IDEAS

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    1. 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.
    2. Adil Bagirov & Asef Ganjehlou, 2008. "An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 187-206, April.
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    Cited by:

    1. Outi Montonen & Kaisa Joki, 2018. "Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints," Journal of Global Optimization, Springer, vol. 72(3), pages 403-429, November.
    2. Outi Montonen & Ville-Pekka Eronen & Timo Ranta & Jani A. S. Huttunen & Marko M. Mäkelä, 2020. "Multiobjective Mixed Integer Nonlinear Model to Plan the Schedule for the Final Disposal of the Spent Nuclear Fuel in Finland," Mathematics, MDPI, vol. 8(4), pages 1-29, April.
    3. 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.
    4. 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.
    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. Mike G. Tsionas, 2021. "Multi-criteria optimization in regression," Annals of Operations Research, Springer, vol. 306(1), pages 7-25, November.
    7. 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.
    8. 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.
    9. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram, 2020. "On q -Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    10. 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.
    11. 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.
    12. 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.

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