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A reduced Jacobian method with full convergence property

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Abstract

In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe (J Optim Theory Appl 179:917–943, 2018) for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant possesses the full convergence property in the sense that the entire sequence converges whenever the objectives are quasiconvex. Simulations are reported showing the performance of this variant compared to RJM and the nondominated sorting genetic algorithm (NSGA-II).

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Notes

  1. These MOPs were selected from the literature, so that the reader can compare our method with others, e.g., the deterministic SQP-like methods experimented in [2, Tables 2–3] (see [1] about dimensions “m”).

  2. Here, the metric \(m_{p,s}\) may be 1/P, 1/HV, GD or CPU, so that all these metrics have the same asymptotic behaviour in a sense that the smaller the measure, the better the solver.

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Acknowledgements

The authors are grateful to the anonymous referees for their considerable comments and suggestions including pertinent remarks and very interesting questions.

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Authors and Affiliations

  1. Department of Mathematics and Computer, Faculty of Sciences Aïn Chock, Hassan II University, BP. 5366, Casablanca, Morocco

    M. El Maghri & Y. Elboulqe

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  1. M. El Maghri
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  2. Y. Elboulqe
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Correspondence to M. El Maghri.

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El Maghri, M., Elboulqe, Y. A reduced Jacobian method with full convergence property. Optim Lett (2024). https://doi.org/10.1007/s11590-023-02083-9

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