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Second Order Cones for Maximal Monotone Operators via Representative Functions

Eberhard, Andrew C. and Borwein, Jonathan M. (2008) Second Order Cones for Maximal Monotone Operators via Representative Functions. Setvalued Analysis, 16 . pp. 157-184.

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    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.

    Item Type: Article
    Additional Information: pubdom FALSE
    Uncontrolled Keywords: Second order cones, maximal monotone operators, Proto–differentiability
    Subjects: 46-xx Functional analysis > 46Nxx Miscellaneous applications of functional analysis
    49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
    46-xx Functional analysis > 46Axx Topological linear spaces and related structures
    47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    Faculty: UNSPECIFIED
    Depositing User: lingyun ye
    Date Deposited: 29 Aug 2007
    Last Modified: 11 Jan 2015 17:53
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/348

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