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A General Formula on the Conjugate of the Difference of Functions

Published online by Cambridge University Press:  20 November 2018

J.-B. Hiriart-Urruty
J.-B. Hiriart-Urruty*
Affiliation:
Laboratoire D'analyse Numérique Université Paul Sabatier 118, Route de Narbonne 31062 Toulouse Cedex, France
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Abstract

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Given an arbitrary function g :X → (-∞, +∞] and a lowersemicontinuous convex function h:X → (-∞, +∞], we give the general expression of the conjugate (g — h)* of g - h in terms of g* and h*. As a consequence, we get Toland's duality theorem:

Keywords

90C2549B
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 482 - 485
Copyright
Copyright © Canadian Mathematical Society 1986

References

References

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Note Added on Proofs: The equalities (2.8) and (2.9) also appear in the following papers:

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