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E′-Convex Sets and Functions: Properties and Characterizations

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Abstract

The main properties of evenly convex sets and functions have been deeply studied by different authors, and a duality theory for evenly convex optimization problems has been well developed as well. In this theory, the notion of \(\text {e}^{\prime }\)-convexity appears as a necessary requirement for obtaining important results in strong and stable strong duality. This fact has motivated the authors to study possible properties of this kind of convexity in sets and functions, which is closely connected to even convexity.

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Acknowledgements

The authors would like to thank the two anonymous reviewers for their constructive comments and pieces of advice. They substantially helped to improve the presentation and understanding of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University of Alicante, Alicante, Spain

    M. D. Fajardo

  2. Department of Physics and Mathematics, University of Alcalá, Alcalá de Henares, Madrid, Spain

    J. Vidal

Authors
  1. M. D. Fajardo
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  2. J. Vidal
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Correspondence to M. D. Fajardo.

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Dedication to Marco Lopez’s 70th birthday.

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Fajardo, M.D., Vidal, J. E′-Convex Sets and Functions: Properties and Characterizations. Vietnam J. Math. 48, 407–423 (2020). https://doi.org/10.1007/s10013-020-00414-2

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