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Subdifferentials of convex functions and sigma-cyclic monotonicity

Published online by Cambridge University Press:  17 April 2009

Aris Daniilidis
Aris Daniilidis
Affiliation:
Laboratorie de Mathématiques Appliquées, CNRS UPRES A 5033, Université de Pau et des Pays de l'Adour, avenue de l'Université, 64000 Pau, France e-mail: aris.daniilidis@univ.pau.fr
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Abstract

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The property of σcyclic monotonicity is proposed here to describe subdifferentials of lsc convex functions that are continuous in their domains. It is shown that all monotone operators in R and all densely defined cyclically monotome operators in Rn share this property. Examples of a densely defined maximal cyclically monotone operator in a Hilbert space and of a subdifferential of a convex lsc function in R2 which are not σ-cyclically monotone operators are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 269 - 276
Copyright
Copyright © Australian Mathematical Society 2000

References

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