C. R. Johnson
"Iterative methods for large scale linear feasibility problems"
Background: Elementary linear algebra, basic properties of
convex sets and convex functions, fundamentals of convex optimization.
(a) Convex optimization problems: convex feasibility problem, linear
feasibility problem, split feasibility problem, linear split feasibility
(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,
(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
(d) Convergence of projection methods.
3: Extrapolated projection methods and their convergence.