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Moreau–Yosida Regularization of Maximal Monotone Operators of Type (D)

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Abstract

We propose a Moreau–Yosida regularization for maximal monotone operators of type (D), in non-reflexive Banach spaces. It generalizes the classical Moreau–Yosida regularization as well as Brezis–Crandall–Pazy’s extension of this regularization to strictly convex (reflexive) Banach spaces with strictly convex duals. Our main results are obtained by making use of recent results by the authors on convex representations of maximal monotone operators in non-reflexive Banach spaces.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil

    Maicon Marques Alves & Benar Fux Svaiter

Authors
  1. Maicon Marques Alves
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  2. Benar Fux Svaiter
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Corresponding author

Correspondence to Benar Fux Svaiter.

Additional information

M. Marques Alves was partially supported by Brazilian CNPq scholarship 140525/2005-0.

B.F. Svaiter was partially supported by CNPq grants 300755/2005-8, 475647/2006-8 and by PRONEX-Optimization.

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Marques Alves, M., Svaiter, B.F. Moreau–Yosida Regularization of Maximal Monotone Operators of Type (D). Set-Valued Anal 19, 97–106 (2011). https://doi.org/10.1007/s11228-010-0137-9

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  • DOI: https://doi.org/10.1007/s11228-010-0137-9

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