 SIGMAOPT SEMINAR
 Speaker: Dr Francisco Aragón 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, 1^{st} Sep 2011
 Abstract:
Basically, a function is Lipschitz continuous if it has a
bounded slope. This notion can be extended to setvalued maps in
different ways. We will mainly focus on one of them: the socalled Aubin
(or Lipschitzlike) 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 setvalued 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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