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Helping You Finding an Appropriate Regularization Process

Abstract

We survey some processes that relate a given function to a more regular function. We examine the compensated convexity process from this point of view and we give a special attention to an infimal convolution approximation generalizing the Moreau approximation which can be applied to nonconvex functions satisfying mild growth conditions.

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Acknowledgements

We would like to thank the three referees for their careful reading of the initial version of our manuscript and for their insightful comments.

Funding

The research of this author is supported by NAFOSTED, under grant: 101.01-2016.27.

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Corresponding author

Correspondence to Huynh Van Ngai.

Additional information

Dedicated to Michel Théra on the occasion of his seventieth birthday.

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Van Ngai, H., Penot, JP. Helping You Finding an Appropriate Regularization Process. Vietnam J. Math. 46, 407–435 (2018). https://doi.org/10.1007/s10013-018-0293-z

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  • DOI: https://doi.org/10.1007/s10013-018-0293-z

Keywords

  • Compensated convexity
  • Convolution
  • Differentiability
  • Infimal convolution
  • Nonsmooth analysis
  • Regularization
  • Subdifferential

Mathematics Subject Classification (2010)

  • 49J52
  • 46N10
  • 46T20