Autoconjugate representers for linear monotone operators

Simple item page
dc.creatorBauschke, Heinz H.
dc.creatorWang, Xianfu
dc.creatorYao, Liangjin
dc.date2008-02-11
dc.date.accessioned2026-07-07T09:19:51Z
dc.date.available2026-07-07T09:19:51Z
dc.descriptionMonotone operators are of central importance in modern optimization and nonlinear analysis. Their study has been revolutionized lately, due to the systematic use of the Fitzpatrick function. Pioneered by Penot and Svaiter, a topic of recent interest has been the representation of maximal monotone operators by so-called autoconjugate functions. Two explicit constructions were proposed, the first by Penot and Zalinescu in 2005, and another by Bauschke and Wang in 2007. The former requires a mild constraint qualification while the latter is based on the proximal average. We show that these two autoconjugate representers must coincide for continuous linear monotone operators on reflexive spaces. The continuity and the linearity assumption are both essential as examples of discontinuous linear operators and of subdifferential operators illustrate. Furthermore, we also construct an infinite family of autoconjugate representers for the identity operator on the real line.
dc.identifierhttps://arxiv.org/abs/0802.1375
dc.identifierhttp://arxiv.org/abs/0802.1375
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154545
dc.subjectFunctional Analysis
dc.subjectOptimization and Control
dc.subject47H05
dc.titleAutoconjugate representers for linear monotone operators
dc.typetext

Files

Collections

arXiv