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On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization

Author

Listed:
  • Andrea Cristofari

    (University of Rome “Tor Vergata”)

  • Marianna Santis

    (Sapienza University of Rome)

  • Stefano Lucidi

    (Sapienza University of Rome)

Abstract

Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of multiobjective optimization, where the aim is that of approximating the efficient set. This calls for a new analysis of the necessary optimality conditions for multiobjective optimization. We explore conditions for sets of points that share the same features of the necessary optimality conditions for single-objective optimization. On the one hand, from a theoretical point of view, these conditions define properties that are necessarily satisfied by the (weakly) efficient set. On the other hand, from an algorithmic point of view, any set that does not satisfy the proposed conditions can be easily improved by using first-order information on some objective functions. We analyse both the unconstrained and the constrained case, giving some examples.

Suggested Citation

  • Andrea Cristofari & Marianna Santis & Stefano Lucidi, 2024. "On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 126-145, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02478-3
    DOI: 10.1007/s10957-024-02478-3
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    References listed on IDEAS

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    1. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 195-227, May.
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