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Versions of Ekeland’s variational principle involving set perturbations

Author

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  • Phan Khanh
  • Dinh Quy

Abstract

We consider Ekeland’s variational principle for multivalued maps. Instead of dealing with directional perturbations in a direction of the positive cone of the image space, we perturb the map under question by a convex subset of the positive cone to get stronger and more general versions. Many example are provided to highlight relations of our results to existing ones, including their advantages. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Phan Khanh & Dinh Quy, 2013. "Versions of Ekeland’s variational principle involving set perturbations," Journal of Global Optimization, Springer, vol. 57(3), pages 951-968, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:951-968
    DOI: 10.1007/s10898-012-9983-3
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    Cited by:

    1. Jing-Hui Qiu & Fei He & Antoine Soubeyran, 2017. "Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem," Post-Print hal-02084464, HAL.
    2. Jing-Hui Qiu & Antoine Soubeyran & Fei He, 2020. "Equilibrium versions of set-valued variational principles and their applications to organizational behavior," Post-Print hal-02465110, HAL.
    3. Le Phuoc Hai & Phan Quoc Khanh & Antoine Soubeyran, 2022. "General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 347-373, October.
    4. T. Q. Bao & S. Cobzaş & A. Soubeyran, 2018. "Variational principles, completeness and the existence of traps in behavioral sciences," Annals of Operations Research, Springer, vol. 269(1), pages 53-79, October.

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