343 research outputs found
A Cyclic Douglas-Rachford Iteration Scheme
In this paper we present two Douglas-Rachford inspired iteration schemes
which can be applied directly to N-set convex feasibility problems in Hilbert
space. Our main results are weak convergence of the methods to a point whose
nearest point projections onto each of the N sets coincide. For affine
subspaces, convergence is in norm. Initial results from numerical experiments,
comparing our methods to the classical (product-space) Douglas-Rachford scheme,
are promising.Comment: 22 pages, 7 figures, 4 table
The Cyclic Douglas-Rachford Method for Inconsistent Feasibility Problems
We analyse the behaviour of the newly introduced cyclic Douglas-Rachford
algorithm for finding a point in the intersection of a finite number of closed
convex sets. This work considers the case in which the target intersection set
is possibly empty.Comment: 13 pages, 2 figures; references updated, figure 2 correcte
Frugal and Decentralised Resolvent Splittings Defined by Nonexpansive Operators
Frugal resolvent splittings are a class of fixed point algorithms for finding
a zero in the sum of the sum of finitely many set-valued monotone operators,
where the fixed point operator uses only vector addition, scalar multiplication
and the resolvent of each monotone operator once per iteration. In the
literature, the convergence analyses of these schemes are performed in an
inefficient, algorithm-by-algorithm basis. In this work, we address this by
developing a general framework for frugal resolvent splitting which
simultaneously covers and extends several important schemes in the literature.
The framework also yields a new resolvent splitting algorithm which is suitable
for decentralised implementation on regular networks.Comment: 14 page
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