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           A. Cegielski
           C. R. Johnson
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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'ski-Mann theorem.
(d) Convergence of projection methods.

Lecture 3: Extrapolated projection methods and their convergence.

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