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Ekeland's ε-variational principle for set-valued mappings

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  • Guang Ya Chen
  • X. X. Huang

Abstract

In this paper, we introduce the concept of approximate solutions for set-valued mappings and provide a sufficient condition for the existence of approximate solutions of set-valued mappings. We obtain an approximate variational principle for set-valued mappings. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Guang Ya Chen & X. X. Huang, 1998. "Ekeland's ε-variational principle for set-valued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 181-186, November.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:2:p:181-186
    DOI: 10.1007/s001860050020
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    Citations

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    Cited by:

    1. T. X. D. Ha, 2005. "Some Variants of the Ekeland Variational Principle for a Set-Valued Map," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 187-206, January.
    2. Behnam Soleimani, 2014. "Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 605-632, August.
    3. X. X. Huang, 2001. "Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 671-684, March.

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