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A relaxed projection method for solving multiobjective optimization problems

Author

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  • Brito, A.S.
  • Cruz Neto, J.X.
  • Santos, P.S.M.
  • Souza, S.S.

Abstract

In this paper, we propose an algorithm for solving multiobjective minimization problems on nonempty closed convex subsets of the Euclidean space. The proposed method combines a reflection technique for obtaining a feasible point with a projected subgradient method. Under suitable assumptions, we show that the sequence generated using this method converges to a Pareto optimal point of the problem. We also present some numerical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:1:p:17-23
    DOI: 10.1016/j.ejor.2016.05.026
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    8. Masao Fukushima, 1983. "An Outer Approximation Algorithm for Solving General Convex Programs," Operations Research, INFORMS, vol. 31(1), pages 101-113, February.
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    Cited by:

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    3. Kerkhove, L.-P. & Vanhoucke, M., 2017. "A parallel multi-objective scatter search for optimising incentive contract design in projects," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1066-1084.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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