Vietnam Journal of Mathematics

, Volume 46, Issue 2, pp 407–435 | Cite as

Helping You Finding an Appropriate Regularization Process

  • Huynh Van Ngai
  • Jean-Paul Penot


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.


Compensated convexity Convolution Differentiability Infimal convolution Nonsmooth analysis Regularization Subdifferential 

Mathematics Subject Classification (2010)

49J52 46N10 46T20 



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 Information

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


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Quy NhonQui NhonVietnam
  2. 2.Sorbonne Universités UPMC Université Paris 6 UMR 7598 Laboratoire Jacques-Louis LionsParisFrance

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