 CARMA OANT SEMINAR
 Speaker: Dr Francisco Aragón Artacho, CARMA, The University of Newcastle
 Title: Walking on real numbers
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 22^{nd} Oct 2012
 Abstract:
Motivated by the desire to visualise large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar walks and for quantitatively measuring their “randomness”.
What to expect: some interesting ideas, many beautiful pictures (including a 108gigapixel picture of π), and some easytounderstand maths.
What you won’t get: too many equations, difficult proofs, or any “real walking”.
This is a joint work with David Bailey, Jon Borwein and Peter Borwein.
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 CARMA SEMINAR
 Speaker: Dr Francisco Aragón Artacho, CARMA, The University of Newcastle
 Title: DouglasRachford: an algorithm that mysteriously solves sudokus and other nonconvex problems
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 21^{st} Jun 2012
 Abstract:
The DouglasRachford algorithm is an iterative method for finding a point in the intersection of two (or more) closed sets. It is wellknown that the iteration (weakly) converges when it is applied to convex subsets of a Hilbert space. Despite the absence of a theoretical justification, the algorithm has also been successfully applied to various nonconvex practical problems, including finding solutions for the eight queens problem, or sudoku puzzles. In particular, we will show how these two problems can be easily modelled.
With the aim providing some theoretical explanation of the convergence in the nonconvex case, we have established a region of convergence for the prototypical nonconvex DouglasRachford iteration which finds a point on the intersection of a line and a circle. Previous work was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.
PS: Bring your hardest sudoku puzzle :)
 Download: Talk slides (4.7 MB)
 [Permanent link]
 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.
 [Permanent link]
