Journal of Global Optimization

, Volume 57, Issue 3, pp 951–968 | Cite as

Versions of Ekeland’s variational principle involving set perturbations

  • Phan Quoc Khanh
  • Dinh Ngoc Quy


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.


Ekeland’s variational principle Set perturbations Pareto minimizers Kuroiwa’s minimizers Minimal elements Relaxed semicontinuity 

Mathematics Subject Classification (2010)

58E30 49J53 90C48 65K10 58E17 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsInternational University of Hochiminh CityHochiminh CityVietnam
  2. 2.Department of MathematicsCantho UniversityCanthoVietnam

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