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On stationarity for nonsmooth multiobjective problems with vanishing constraints

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Abstract

The aim of this paper is to develop first-order necessary and sufficient optimality conditions for nonsmooth multiobjective optimization problems with vanishing constraints. First of all, we introduce some data qualifications for the problem, and derive the comparisons between them. Secondly, based on the mentioned qualifications, we demonstrate some necessary optimality conditions, named strongly stationary conditions, at weakly efficient and efficient solutions of considered problem. Then, we show that the strongly stationary conditions are also sufficient for optimality. Finally, using the tightened problems, we establish other classes of qualifications and stationary conditions.

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Acknowledgements

The authors would like to express their gratitude to anonymous referee for helpful comments on this paper. This research was in part supported by a Grant from “Iran National Science Foundation: INSF” (No. 98021095).

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Authors and Affiliations

  1. Department of Mathematics, Yazd branch, Islamic Azad University, Yazd, Iran

    Ali Sadeghieh

  2. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

    Nader Kanzi

  3. Department of Economic, University of Messina, Via dei Verdi 75, 98122, Messina, Italy

    Giuseppe Caristi & David Barilla

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  1. Ali Sadeghieh
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  2. Nader Kanzi
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  3. Giuseppe Caristi
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  4. David Barilla
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Correspondence to Nader Kanzi.

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Sadeghieh, A., Kanzi, N., Caristi, G. et al. On stationarity for nonsmooth multiobjective problems with vanishing constraints. J Glob Optim 82, 929–949 (2022). https://doi.org/10.1007/s10898-021-01030-1

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  • DOI: https://doi.org/10.1007/s10898-021-01030-1

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