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Legendre-type integrands and convex integral functions

Borwein, Jonathan M. and Yao, Liangjin (2014) Legendre-type integrands and convex integral functions. Journal of Convex Analysis, 21 (1). pp. 264-288. ISSN 0944-6532

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    Abstract

    In this paper, we study the properties of integral functionals induced on $L^1(S;E)$ by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counterexample

    Item Type: Article
    Subjects: 28-xx Measure and integration
    46-xx Functional analysis > 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
    49-xx Calculus of variations and optimal control; optimization > 49Kxx Necessary conditions and sufficient conditions for optimality
    Faculty: UNSPECIFIED
    Depositing User: Jonathan Borwein
    Date Deposited: 10 Nov 2012 08:48
    Last Modified: 19 Nov 2014 21:59
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1455

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