• Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Dates: 9:30 am, Tue, 28th Jul 2015 - 11:00 am, Tue, 28th Jul 2015

  • Jon's talk will be 60 minutes, followed by 30 minutes for Yves.

  • Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
  • Title: Monotone inclusions and Fitzpatrick functions

    We study maximal monotone inclusions from the perspective of (convex) gap functions.

    We propose a very natural gap function and will demonstrate how this function arises from the Fitzpatrick function — a convex function used effectively to represent maximal monotone operators.

    This approach allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion.

    • We also study the special cases of a variational inequality and of a generalised variational inequality problem.
    • The associated notion of a scalar gap is also considered.
    • Corresponding local and global error bounds are developed for the maximal monotone inclusion.

    This is joint work with Joydeep Dutta.

  • Speaker: Yves Lucet, University of British Colombia
  • Title: On the convexity of piecewise-defined functions

    Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components – when can we conclude that the entire function is convex? Our main result provides sufficient conditions for a piecewise-defined function f to be convex. We also provide a sufficient condition for checking the convexity of a piecewise linear-quadratic function, which play an important role in computer-aided convex analysis.

    Based on joint work with Heinz H. Bauschke (Mathematics, UBC Okanagan) and Hung M. Phan (Mathematics, University of Massachusetts Lowell).

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