Abstract
In this paper, we establish necessary and sufficient conditions to characterize weakly efficient solutions in nonsmooth quasiconvex multiobjective programming. The results are proved in terms of the Greenberg–Pierskalla, Penot, Plastria, Gutiérrez and Suzuki–Kuroiwa subdifferentials. The established results can be used to provide powerful tools for sketching numerical algorithms and deriving duality results.
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Acknowledgements
The authors would like to express their gratitude to the editor in chief of JOGO, handling editor, and anonymous referee for their helpful comments on the earlier versions of the paper. The work of the second author was in part supported by the Iran National Science Foundation (INSF) (Grant 98009933).
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Kanzi, N., Soleimani-damaneh, M. Characterization of the weakly efficient solutions in nonsmooth quasiconvex multiobjective optimization. J Glob Optim 77, 627–641 (2020). https://doi.org/10.1007/s10898-020-00893-0
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DOI: https://doi.org/10.1007/s10898-020-00893-0
Keywords
- Quasiconvex function
- Multiobjective programming
- Nonsnmooth optimization
- Constraint qualification
- Optimality conditions