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Applications of Convex Analysis within Mathematics

Aragón Artacho, Francisco J. and Borwein, Jonathan M. and Martín-Márquez, Victoria and Yao, Liangjin (2014) Applications of Convex Analysis within Mathematics. Mathematical Programming, 148 (1-2). pp. 49-88.

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    Abstract

    In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.

    Item Type: Article
    Subjects: 47-xx Operator theory > 47Bxx Special classes of linear operators
    47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    47-xx Operator theory > 47Nxx Miscellaneous applications of operator theory
    90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 06 Jan 2015 10:12
    Last Modified: 06 Jan 2015 10:12
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1513

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