Colóquio do Departamento
de Matemática - 2021/1
Página Atualizada:
3a-feira, 23 de Novembro de 2021
Próximo Colóquio
26 de Novembro de 2021, 14:00h
Prof. Dr. Luiz-Rafael Santos
(UFSC-Blumenau)
Infeasibility and error bound imply
finite convergence of alternating projections
Abstract: In this work we
combine two ingredients in order to get
a rather
surprising result on one of the
most studied, elegant, and powerful
tools for solving convex feasibility problems, the method
of alternating
projections (MAP). Going back to names such
as Kaczmarz and von Neumann,
MAP has the ability to
track a pair of points realizing minimum distance
between
two given closed convex sets. Unfortunately, MAP may suffer from
arbitrarily slow convergence, and sublinear rates are essentially
only
surpassed in the presence of some Lipschitzian error bound, which
is our
first
ingredient. The second one is a seemingly
unfavorable and
unexpected condition, namely, infeasibility. For two non-intersecting
closed
convex sets satisfying an error bound,
we establish finite
convergence of MAP. Moreover, the farther the
target sets lie from each
other,
fewer are the iterations needed by MAP for finding a best
approximation pair. Insightful examples and further
theoretical and
algorithmic discussions accompany
our results, including the
investigation of finite termination of other projection methods..
|
Data |
Palestrante |
Afiliaçao |
Título da Palestra / Slides da Apresentação |
|
|
17/dez/2021 |
Prof.
Dr. Paulo Teotônio Sobrinho |
TBA |
||
|
10/dez/2021 |
Prof.
Dr. Carlile Campos Lavor |
Geometria
de Distâncias e COVID-19 |
||
|
03/dez/2021 |
Prof.
Dr. Ivan Pontual Costa e Silva |
Modelagem
geométrica do colapso gravitacional. |
||
|
26/nov/2021 |
Prof.
Dr. Luiz Rafael dos Santos |
Infeasibility and error
bound imply finite convergence of alternating projections |
||
|
19/nov/2021 |
Prof.
Dr. Mikhailo Dokuchaev |
Ruy
Exel Filho: um impacto científico. |
||
|
12/nov/2021 |
Prof.
Dr. Dennis Fernandes Alves Bessada |
Cancelado/
Novo seminário apresentado pelo organizador do Colóquio. |
||
|
05/nov/2021 |
Prof.
Dr. Marcelo M.S. Alves |
Representações
parciais de álgebras de Hopf. |
||
|
29/out/2021 |
Prof.
Dr. Marcus Sarkis-Martins |
Introduction to Domain Decomposition
Methods. |
||
|
22/out/2021 |
Prof.
Dr. Eduardo V. Teixeira |
EDPs elípticas no Brasil: a Escola de Djairo
de Figueiredo. |
||
|
15/out/2021 |
Prof.
Dr. Carlos G.T.A. Moreira |
Sobre
a Matemática de Jacob Palis. |
||
|
08/out/2021 |
Prof.
Dr. Pedro Peixoto |
Challenges of mathematical
and numerical modeling of the
atmosphere dynamics. |
||
|
01/out/2021 |
Prof.
Dr. Ronaldo Garcia |
Contribuições
de Maurício Peixoto aos Sistemas Dinâmicos e às EDO's. |
||
|
24/set/2021 |
Prof.
Dr. Paulo J.S. Silva |
A
otimização como ferramenta contra a COVID-19 |
||
|
17/set/2021 |
Prof.
Dr. Gregório Pacelli F. Bessa |
A
Matemática no Ceará |
||
|
10/set/2021 |
Prof.
Dr. Gregório Malajovich |
Visões
do Infinito. |
||