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A new reduced gradient method for solving linearly constrained multiobjective optimization problems

Author

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  • Mustapha El Moudden

    (Moulay Ismail University)

  • Ahmed El Ghali

    (Moulay Ismail University)

Abstract

In this paper, we consider the linearly constrained multiobjective minimization, and we propose a new reduced gradient method for solving this problem. Our approach solves iteratively a convex quadratic optimization subproblem to calculate a suitable descent direction for all the objective functions, and then use a bisection algorithm to find an optimal stepsize along this direction. We prove, under natural assumptions, that the proposed algorithm is well-defined and converges globally to Pareto critical points of the problem. Finally, this algorithm is implemented in the MATLAB environment and comparative results of numerical experiments are reported.

Suggested Citation

  • Mustapha El Moudden & Ahmed El Ghali, 2018. "A new reduced gradient method for solving linearly constrained multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 719-741, December.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:3:d:10.1007_s10589-018-0023-1
    DOI: 10.1007/s10589-018-0023-1
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    References listed on IDEAS

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    1. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    2. H. P. Benson & G. M. Boger, 2000. "Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 301-322, February.
    3. 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.
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    Cited by:

    1. 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.

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