• Speaker: Dr Francisco Arag√≥n Artacho, CARMA, The University of Newcastle
  • Title: Lipschitzian properties of a generalized proximal point algorithm
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UNewcastle [ENQUIRIES]
  • Time and Date: 4:00 pm, Thu, 1st Sep 2011
  • Abstract:

    Basically, a function is Lipschitz continuous if it has a bounded slope. This notion can be extended to set-valued maps in different ways. We will mainly focus on one of them: the so-called Aubin (or Lipschitz-like) property. We will employ this property to analyze the iterates generated by an iterative method known as the proximal point algorithm. Specifically, we consider a generalized version of this algorithm for solving a perturbed inclusion $$y \in T(x),$$ where $y$ is a perturbation element near 0 and $T$ is a set-valued mapping. We will analyze the behavior of the convergent iterates generated by the algorithm and we will show that they inherit the regularity properties of $T$, and vice versa. We analyze the cases when the mapping $T$ is metrically regular (the inverse map has the Aubin property) and strongly regular (the inverse is locally a Lipschitz function). We will not assume any type of monotonicity.

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