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Limits of maximal monotone operators driven by their representative functions

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Abstract

In a previous paper, the authors showed that in a reflexive Banach space the lower limit of a sequence of maximal monotone operators is always representable by a convex function. The present paper gives precisions to the latter result by demonstrating the continuity of the representation with respect to the epi-convergence of the representative functions, and the stability of the class of maximal monotone operators with respect to the Mosco-convergence of their representative functions.

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Acknowledgements

The authors gratefully acknowledge the anonymous referees for their comments which allowed an improvement of the presentation of the paper. This work was supported by Cienciactiva-Concytec EE020-MATH Amsud Project Nro.003-2017 and by MATH Amsud 17-MATH-06.

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Authors and Affiliations

  1. Universidad del Pacífico, Lima, Peru

    Yboon García

  2. Université des Antilles, Guadeloupe, France

    Marc Lassonde

  3. LIMOS, Clermont-Ferrand, France

    Marc Lassonde

Authors
  1. Yboon García
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  2. Marc Lassonde
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Correspondence to Marc Lassonde.

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García, Y., Lassonde, M. Limits of maximal monotone operators driven by their representative functions. Optim Lett 13, 795–803 (2019). https://doi.org/10.1007/s11590-018-1279-1

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  • DOI: https://doi.org/10.1007/s11590-018-1279-1

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