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Integration of the Fenchel Subdifferentials Revisited

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Abstract

We obtain a simple integration formula for the Fenchel subdifferentials on Euclidean spaces and analyze some of its consequences. For functions defined on locally convex spaces, we present a similar result in terms of 𝜖-subdifferentials.

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Acknowledgments

I am very grateful to two anonymous referees for their helpful remarks; I feel particularly indebted to the one who pointed out that the intial version needed several important corrections.

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Authors and Affiliations

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

    Juan Enrique Martínez-Legaz

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  1. Juan Enrique Martínez-Legaz
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Correspondence to Juan Enrique Martínez-Legaz.

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Dedicated to Professor Boris Mordukhovich on his 65th birthday.

This research 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). The author is affiliated to MOVE (Markets, Organizations and Votes in Economics).

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Martínez-Legaz, J.E. Integration of the Fenchel Subdifferentials Revisited. Vietnam J. Math. 42, 533–542 (2014). https://doi.org/10.1007/s10013-014-0101-3

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  • DOI: https://doi.org/10.1007/s10013-014-0101-3

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