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On the Existence of a Saddle Value

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Abstract

In this work, we achieve a complete characterization of the existence of a saddle value, for bifunctions which are convex, proper, and lower semi continuous in their first argument, by considering new suitably defined notions of special directions of recession. As special cases, we obtain some recent results of Lagrangian duality theory on zero duality gap for convex programs.

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Acknowledgments

The research of the corresponding author was supported by the MICINN of Spain, Grant MTM2011-29064-C03-01, and under Australian Research Council’s Discovery Projects funding scheme (project number DP140103213). He is affiliated to MOVE (Markets, Organizations and Votes in Economics). The authors are grateful to Michel Volle for valuable remarks, which have helped us to substantially improve the manuscript.

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Authors and Affiliations

  1. Dipartimento di Economia e Management, Università degli Studi di Brescia, Contrada Santa Chiara 50, 25122, Brescia, Italy

    F. Bonenti

  2. Departament d’Economia i d’Història Econòmica, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    J. E. Martínez-Legaz

Authors
  1. F. Bonenti
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  2. J. E. Martínez-Legaz
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Corresponding author

Correspondence to J. E. Martínez-Legaz.

Additional information

Communicated by Stefan Rolewicz.

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Bonenti, F., Martínez-Legaz, J.E. On the Existence of a Saddle Value. J Optim Theory Appl 165, 785–792 (2015). https://doi.org/10.1007/s10957-014-0665-9

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  • DOI: https://doi.org/10.1007/s10957-014-0665-9

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