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Understanding the Quasi Relative Interior

Lindstrom, Scott (2015) Understanding the Quasi Relative Interior. Project Report. Permanent Reserve at Portland State University Mathematics Department Libary. (Submitted)

[img] PDF (A discussion of an article by J.M. Borwein and A.S. Lewis on the topic of quasi relative interiors and Fenchel duality) - Accepted Version
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    Abstract

    This paper undertakes to analyze and explain the paper "Partially Fnite Convex Programming, Part I: Quasi Relative Interiors and Duality Theory" by authors J.M. Borwein and A.S. Lewis. It begins with an overview of some basic notions of convex analysis and goes on to address the challenges which motivate the development of the principle concept discussed therein, namely the quasi-relative interior. It goes on to provide an overview of the notion of the convex conjugate with several illustrative examples. It reproduces and explains the major results of the article with a level of detail easily understood by a graduate level analysis student. For ease of reference, it closely follows the order of the original paper.

    Item Type: Monograph (Project Report)
    Subjects: 46-xx Functional analysis > 46Cxx Inner product spaces and their generalizations, Hilbert spaces
    46-xx Functional analysis > 46Txx Nonlinear functional analysis
    49-xx Calculus of variations and optimal control; optimization > 49Kxx Necessary conditions and sufficient conditions for optimality
    52-xx Convex and discrete geometry > 52Axx General convexity
    Faculty: UNSPECIFIED
    Depositing User: Scott Lindstrom
    Date Deposited: 01 Mar 2016 09:54
    Last Modified: 01 Mar 2016 09:54
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1682

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