منابع مشابه
Relaxed Alternating Projection Methods
In this paper we deal with the von Neumann alternating projection method xk+1 = PAPBxk and with its generalization of the form xk+1 = PA(xk + k(PAPBxk xk)), where A;B are closed and convex subsets of a Hilbert space H and FixPAPB 6= ?. We do not suppose that A \ B 6= ?. We give su¢ cient conditions for the weak convergence of the sequence (xk) to FixPAPB in the general case and in the case A is...
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We propose and study a block-iterative projections method for solving linear equations and/or inequalities. The method allows diagonal component-wise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonally-relaxed orthogonal projections (DROP). Diagonal relaxation has proven useful in accelerating the initial convergence...
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The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction...
متن کاملAlternating minimization and projection methods for structured nonconvex problems
We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: L(x, y) = f(x)+Q(x, y)+g(y), where f : R → R∪{+∞} and g : R → R∪{+∞} are proper lower semicontinuous functions, and Q : R × R → R is a smooth C function which couples the variables x and y. The algorithm can be viewed as a proximal regularization of the usual Gau...
متن کاملAlternating Projection Methods - Failure in the Absence of Convexity
Given an initial point, x0, sets Si for i = 1, . . . , r and their corresponding nearest point projections PSi , the method of alternating projections (MAP) attempts to finds a point in ∩i=1Si by cyclically projecting onto the sets. The original alternating projection result was due to von Neumann (1933) who was able to prove that if the sets are subspaces MAP converges in norm to P∩i=1Si . Usi...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2008
ISSN: 1052-6234,1095-7189
DOI: 10.1137/070698750