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Versions of Ekeland’s variational principle involving set perturbations

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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.

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Authors and Affiliations

  1. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    Phan Quoc Khanh

  2. Department of Mathematics, Cantho University, Cantho, Vietnam

    Dinh Ngoc Quy

Authors
  1. Phan Quoc Khanh
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  2. Dinh Ngoc Quy
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Correspondence to Dinh Ngoc Quy.

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Khanh, P.Q., Quy, D.N. Versions of Ekeland’s variational principle involving set perturbations. J Glob Optim 57, 951–968 (2013). https://doi.org/10.1007/s10898-012-9983-3

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  • DOI: https://doi.org/10.1007/s10898-012-9983-3

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