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Optimality conditions and minimax properties in set optimization

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Abstract

In this paper, we consider a generalization of the Gerstewitz’s function to present several optimality conditions and existence theorems for a set optimization problem without convexity assumptions. A characterization of set solutions for a set-valued optimization problem is given via minimax inequalities.

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Acknowledgements

This research was partially supported by project ETSI Industriales (UNED) 2018-MAT11.

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Authors and Affiliations

  1. Universidad Nacional de Educación a Distancia, Juan del Rosal, 12, 28040, Madrid, Spain

    María Alonso, Elvira Hernández & Elena Pereira

Authors
  1. María Alonso
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  2. Elvira Hernández
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  3. Elena Pereira
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Correspondence to Elvira Hernández.

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Alonso, M., Hernández, E. & Pereira, E. Optimality conditions and minimax properties in set optimization. Optim Lett 13, 55–68 (2019). https://doi.org/10.1007/s11590-018-1244-z

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  • DOI: https://doi.org/10.1007/s11590-018-1244-z

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