The problem of optimal smoothing for convex functions
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- by Mohammad Ghomi
- Proc. Amer. Math. Soc. 130 (2002), 2255-2259
- DOI: https://doi.org/10.1090/S0002-9939-02-06743-6
- Published electronically: March 25, 2002
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Abstract:
A procedure is described for smoothing a convex function which not only preserves its convexity, but also, under suitable conditions, leaves the function unchanged over nearly all the regions where it is already smooth. The method is based on a convolution followed by a gluing. Controlling the Hessian of the resulting function is the key to this process, and it is shown that it can be done successfully provided that the original function is strictly convex over the boundary of the smooth regions.References
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Bibliographic Information
- Mohammad Ghomi
- Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
- MR Author ID: 687341
- Email: ghomi@math.sc.edu
- Received by editor(s): December 19, 1999
- Published electronically: March 25, 2002
- Communicated by: Bennett Chow
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2255-2259
- MSC (2000): Primary 26B25, 52A41
- DOI: https://doi.org/10.1090/S0002-9939-02-06743-6
- MathSciNet review: 1896406