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A formula on the subdifferential of the deconvolution of convex functions

Published online by Cambridge University Press:  17 April 2009

M. Volle
M. Volle
Affiliation:
University of Avignon, 33 rue L Pasteur, 84000 Avignon, France
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Abstract

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It is known that, under suitable assumptions, the subdifferential ∂(f □ g) of the infimal convolution of two convex functions f and g coincides with the parallel sum of ∂ f and ∂ g. We prove that a similar formula holds for the subdifferential of the deconvolution of two convex functions: under appropriate hypothesis it coincides with the parallel star-difference of the sub-differentials of the functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 2 , April 1993 , pp. 333 - 340
Copyright
Copyright © Australian Mathematical Society 1993

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