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 | References | Similar Articles | Additional Information

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:
http://dx.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