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An augmented Lagrangian algorithm for multi-objective optimization

Author

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  • G. Cocchi

    (Università degli Studi di Firenze)

  • M. Lapucci

    (Università degli Studi di Firenze)

Abstract

In this paper, we propose an adaptation of the classical augmented Lagrangian method for dealing with multi-objective optimization problems. Specifically, after a brief review of the literature, we give a suitable definition of Augmented Lagrangian for equality and inequality constrained multi-objective problems. We exploit this object in a general computational scheme that is proved to converge, under mild assumptions, to weak Pareto points of such problems. We then provide a modified version of the algorithm which is more suited for practical implementations, proving again convergence properties under reasonable hypotheses. Finally, computational experiments show that the proposed methods not only do work in practice, but are also competitive with respect to state-of-the-art methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:77:y:2020:i:1:d:10.1007_s10589-020-00204-z
    DOI: 10.1007/s10589-020-00204-z
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    Cited by:

    1. Matteo Lapucci & Pierluigi Mansueto, 2023. "A limited memory Quasi-Newton approach for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 85(1), pages 33-73, May.

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