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The problem of optimal smoothing for convex functions


Author: Mohammad Ghomi
Journal: Proc. Amer. Math. Soc. 130 (2002), 2255-2259
MSC (2000): Primary 26B25, 52A41
Published electronically: March 25, 2002
MathSciNet review: 1896406
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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.


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Additional Information

Mohammad Ghomi
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email: ghomi@math.sc.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06743-6
Keywords: Convex function, convolution, smooth approximation, mollifier
Received by editor(s): December 19, 1999
Published electronically: March 25, 2002
Communicated by: Bennett Chow
Article copyright: © Copyright 2002 American Mathematical Society