• Speaker: Prof Dominikus Noll, Institut de Mathématiques , Université Paul Sabatier
  • Title: Convergence of descent methods using the Kurdyka-Lojasiewicz inequality
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 10:00 am, Thu, 20th Feb 2014
  • To be received via videoconferencing.
  • Abstract:

    Without convexity the convergence of a descent algorithm can normally only be certified in the weak sense that every accumulation point of the sequence of iterates is critical. This does not at all correspond to what we observe in practice, where these optimization methods always converge to a single limit point, even though convergence may sometimes be slow.

    Around 2006 it has been observed that convergence to a single limit can be proved for objective functions having certain analytic features. The property which is instrumental here is called the Lojasiewicz inequality, imported from analytic function theory. While this has been successfully applied to smooth functions, the case of non-smooth functions turns out more difficult. In this talk we obtain some progress for upper-C1 functions. Then we proceed to show that this is not just out of a theoretical sandpit, but has consequences for applications in several fields. We sketch an application in destructive testing of laminate materials.

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