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Boundary of Maximal Monotone Operators Values

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Abstract

We characterize in Hilbert spaces the boundary of the values of maximal monotone operators, by means only of the values at nearby points, which are close enough to the reference point but distinct of it. This allows to write the values of such operators using finite convex combinations of the values at at most two nearby points. We also provide similar characterizations for the normal cone to prox-regular sets.

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Acknowledgements

We would like to thank two anonymous referees for their careful reading and for providing valuable suggestions and observations which allowed us to improve the manuscript.

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Authors and Affiliations

  1. Center for Mathematical Modeling, Universidad de Chile, Santiago, Chile

    Abderrahim Hantoute

  2. Universidad de O’Higgins, Rancagua, Chile

    Bao Tran Nguyen

Authors
  1. Abderrahim Hantoute
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  2. Bao Tran Nguyen
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Corresponding author

Correspondence to Abderrahim Hantoute.

Additional information

Research partially supported by projects Fondecyt-Conicyt No. 1151003, Conicyt-Pcha/Doctorado Nacional/2014-63140104, Mathamsud 17-Math-06, Conicyt-Redes No. 150040, and Conicyt PIA/concurso apoyo a centros científicos y tecnológicos de excelencia con financiamiento BASAL AFB170001.

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Hantoute, A., Nguyen, B.T. Boundary of Maximal Monotone Operators Values. Appl Math Optim 82, 225–243 (2020). https://doi.org/10.1007/s00245-018-9498-5

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  • DOI: https://doi.org/10.1007/s00245-018-9498-5

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