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Set-Valued Analysis

, Volume 16, Issue 2–3, pp 157–184 | Cite as

Second Order Cones for Maximal Monotone Operators via Representative Functions

  • A. C. EberhardEmail author
  • J. M. Borwein
Article

Abstract

It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the Graph T. In particular we obtain formula for the proto-derivative, as well as its polar, the normal cone to the graph of T. First order derivatives are shown to be useful in recognising points of single-valuedness of T. We show that a strong form of proto-differentiability to the graph of T, is often associated with single valuedness of T.

Keywords

Second order cones Maximal monotone operators Proto-differentiability 

Mathematics Subject Classifications (2000)

47H05 46N10 47H04 46A20 49J53 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of Mathematical and Geospatial SciencesRMIT UniversityMelbourneAustralia
  2. 2.Faculty of Computing ScienceDalhousie UniversityHalifaxCanada

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