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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco

    Mustapha El Moudden & Ahmed El Ghali

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  1. Mustapha El Moudden
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  2. Ahmed El Ghali
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Correspondence to Mustapha El Moudden.

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El Moudden, M., El Ghali, A. A new reduced gradient method for solving linearly constrained multiobjective optimization problems. Comput Optim Appl 71, 719–741 (2018). https://doi.org/10.1007/s10589-018-0023-1

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  • DOI: https://doi.org/10.1007/s10589-018-0023-1

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