Relaxed Alternating Projection Methods

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Relaxed Alternating Projection Methods
Let A and B be nonempty, convex and closed subsets of a Hilbert space H. In the practical considerations we need to find an element of the intersection A B or, more general, to solve the following problem: find a A and b B such that a - b = inf aA,bB a - b . One of the important methods generating sequences which converge weakly to a solution of above problems is the von Neumann alternating projection method xk+1 = PAPBxk. The method has found application in different areas of mathematics. These include probability and statistics, image reconstruction and intensity modulated radiation therapy, where the convex subsets are described by a large and sparse system of linear equations or inequalities. We deal with generalization of the von Neumann alternating projection method of the form xk+1 = PA(xk + k(xk)(PAPBxk - xk)), where Fix PAPB = . We give sufficient conditions for the weak convergence of the sequence (xk) to Fix PAPB in the general case and in the case A is a closed affine sub...
Andrzej Cegielski, Agnieszka Suchocka
Added 28 Dec 2010
Updated 28 Dec 2010
Type Journal
Year 2008
Authors Andrzej Cegielski, Agnieszka Suchocka
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