DocServer

A characterization of Bregman firmly nonexpansive operators using a new monotonicity concept.

Borwein, Jonathan M. and Reich, S. and Sabach, S. (2011) A characterization of Bregman firmly nonexpansive operators using a new monotonicity concept. J. Nonlinear and Convex Analysis, 12 . pp. 161-183.

[img]
Preview
PDF - Accepted Version
Download (294Kb) | Preview

    Abstract

    The property of nonexpansivity (1-Lipschitz) is very important in the analysis of many optimization problems. In this paper we study a more general notion of nonexpansivity – Bregman nonexpansivity. We present a characterization of Bregman firmly nonexpansive operators in general reflexive Banach spaces. This characterization allows us to construct Bregman firmly nonexpansive operators explicitly. We provide several examples of such operators with respect to the Boltzmann-Shannon entropy and the Fermi-Dirac entropy in Euclidean spaces. We also compute resolvents with respect to these functions

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 29 Oct 2012 17:33
    Last Modified: 05 Jan 2015 15:21
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1445

    Actions (login required)

    View Item