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Infimal convolutions and lipschitzian properties of subdifferentials for prox-regular functions in hilbert spaces

Bačak, Miroslav and Borwein, Jonathan M. and Eberhard, Andrew and Mordukhovich, Boris S. (2010) Infimal convolutions and lipschitzian properties of subdifferentials for prox-regular functions in hilbert spaces. Journal of Convex Analysis, 17 (3-4). pp. 737-763.

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    Abstract

    We study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to the rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new subdifferential properties of infimal convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) subdifferentials of prox-regular functions forces such functions, under weak assumptions, actually to be locally smooth with single-valued subdifferentials reduced to Lipschitz continuous gradient mappings.

    Item Type: Article
    Uncontrolled Keywords: subdifferentials, Lipschitz continuity, infimal convolutions, prox-regular functions, prox-bounded functions, set-valued mappings
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 05 Jan 2015 15:31
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1224

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