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Subdifferentiation of Regularized Functions

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Abstract

We study the Moreau regularization process for functions satisfying a general growth condition on general Banach spaces. We give differentiability criteria and we study the relationships between the subdifferentials of the function and the subdifferentials of its approximations. We also consider the Lasry-Lions process.

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Authors and Affiliations

  1. Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam

    Huynh Van Ngai

  2. Sorbonne Universités UPMC Université Paris 6 UMR 7598 Laboratoire Jacques-Louis Lions, 75005, Paris, France

    Jean-Paul Penot

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  1. Huynh Van Ngai
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  2. Jean-Paul Penot
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Correspondence to Jean-Paul Penot.

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Dedicated to Lionel Thibault

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Van Ngai, H., Penot, JP. Subdifferentiation of Regularized Functions. Set-Valued Var. Anal 24, 167–189 (2016). https://doi.org/10.1007/s11228-016-0367-6

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