Home
Program
Announcement
Organizers
Invited speakers
Invited
lectures
A. Cegielski
C. R. Johnson
Fees
Deadlines
Participants
Previous workshops
Contact

INVITED LECTURES
Andrzej Cegielski
"Iterative methods for large scale linear feasibility problems"
Necessary
Background: Elementary linear algebra, basic properties of
convex sets and convex functions, fundamentals of convex optimization.
Lecture
1:
(a) Convex optimization problems: convex feasibility problem, linear
feasibility problem, split feasibility problem, linear split feasibility
problem.
(b) Examples of applications.
(c) Algorithmic operators and their properties: nonexpansive
operators, firmly nonexpansive operators, relaxed firmly nonexpansive
operators, averaged operators, strongly quasi nonexpansive operators,
separating operators.
Lecture
2: (a) Projection methods: von Neumann method of alternative projection,
Kaczmarz method of cyclic projection, Cimmino method of simultaneous
projection, Landweber method, projected Landweber method.
(b) Examples of metric projection.
(c) Convergence theorems: Opial's theorem, Krasnosel'skiMann
theorem.
(d) Convergence of projection methods.
Lecture
3: Extrapolated projection methods and their convergence.
