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Meetings with Lambert W and Other Special Functions in Optimization and Analysis

Borwein, Jonathan M. and Lindstrom, Scott (2016) Meetings with Lambert W and Other Special Functions in Optimization and Analysis. Pure and Applied Functional Analysis . (In Press)

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    Abstract

    We remedy the under-appreciated role of the Lambert W function in convex analysis and optimization. We �rst discuss the role of little-known special functions in optimization and then illustrate the relevance of W in a series problem posed by Donald Knuth. We then provide a basic overview of the convex analysis of W and go on to explore its role in duality theory where it appears quite naturally in the closed forms of the convex conjugates for certain functions. We go on to discover a useful class of functions for which this is the case and investigate their use in optimization, providing some code and examples.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 27 Jun 2016 12:05
    Last Modified: 27 Jun 2016 12:05
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1705

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