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General Ekeland's Variational Principle for Set-Valued Mappings

Author

Listed:
  • G. Y. Chen

    (Academia Sinica)

  • X. X. Huang

    (Chongqing Normal University)

  • S. H. Hou

    (Hong Kong Polytechnic University)

Abstract

In this paper, we introduce the concept of approximate solutions for set-valued optimization problems. A sufficient condition for the existence of approximate solutions is obtained. A general Ekeland's variational principle for set-valued mappings in complete ordered metric spaces and complete metric spaces are derived. These results are generalizations of results for vector-valued functions in Refs. 1–4.

Suggested Citation

  • G. Y. Chen & X. X. Huang & S. H. Hou, 2000. "General Ekeland's Variational Principle for Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 151-164, July.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:1:d:10.1023_a:1004663208905
    DOI: 10.1023/A:1004663208905
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    References listed on IDEAS

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    1. G. Y. Chen & X. X. Huang, 1998. "A unified approach to the existing three types of variational principles for vector valued functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(3), pages 349-357, December.
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    Cited by:

    1. Qamrul Hasan Ansari & Andreas H Hamel & Pradeep Kumar Sharma, 2020. "Ekeland’s variational principle with weighted set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 117-136, February.

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    1. X. X. Huang, 2000. "Extended Well-Posedness Properties of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 165-182, July.
    2. 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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