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On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings

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  • P. Khanh
  • D. Quy

Abstract

We propose a very weak type of generalized distances called a weak τ-function and use it to weaken the assumptions about lower semicontinuity in existing versions of Ekeland’s variational principle and equivalent formulations. Copyright Springer Science+Business Media, LLC. 2011

Suggested Citation

  • P. Khanh & D. Quy, 2011. "On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings," Journal of Global Optimization, Springer, vol. 49(3), pages 381-396, March.
    • Handle: RePEc:spr:jglopt:v:49:y:2011:i:3:p:381-396
    DOI: 10.1007/s10898-010-9565-1
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    Citations

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    Cited by:

    1. Takashi Maeda, 2012. "On Optimization Problems with Set-Valued Objective Maps: Existence and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 263-279, May.
    2. P. Q. Khanh & D. N. Quy, 2012. "On Ekeland’s Variational Principle for Pareto Minima of Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 280-297, May.
    3. T. Q. Bao & B. S. Mordukhovich & A. Soubeyran, 2015. "Variational Analysis in Psychological Modeling," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 290-315, January.
    4. L. P. Hai & L. Huerga & P. Q. Khanh & V. Novo, 2019. "Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems," Journal of Global Optimization, Springer, vol. 74(2), pages 361-382, June.
    5. Le Phuoc Hai, 2021. "Ekeland variational principles involving set perturbations in vector equilibrium problems," Journal of Global Optimization, Springer, vol. 79(3), pages 733-756, March.
    6. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.
    7. Q. Q. Song & G. Q. Tang & L. S. Wang, 2013. "On Essential Stable Sets of Solutions in Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 591-599, March.
    8. Yuqing Chen & Chuangliang Zhang, 2018. "On the Weak Semi-continuity of Vector Functions and Minimum Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 119-130, July.

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