A note on the finite convergence of alternating projections

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality, which until now has been restricted to sets with nonempty int...

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Main Authors: Bui, Hoa, Loxton, Ryan, Moeini, A.
Format: Journal Article
Language:English
Published: ELSEVIER 2021
Subjects:
Online Access:http://purl.org/au-research/grants/arc/IC180100030
http://hdl.handle.net/20.500.11937/89492
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author Bui, Hoa
Loxton, Ryan
Moeini, A.
author_facet Bui, Hoa
Loxton, Ryan
Moeini, A.
author_sort Bui, Hoa
building Curtin Institutional Repository
collection Online Access
description We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality, which until now has been restricted to sets with nonempty intersection. In the special case of a polyhedron and closed half space, our sufficient conditions define the minimum distance between the two sets that is required for alternating projections to converge in a single iteration.
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spelling curtin-20.500.11937-894922024-02-15T09:53:55Z A note on the finite convergence of alternating projections Bui, Hoa Loxton, Ryan Moeini, A. Science & Technology Technology Operations Research & Management Science Alternating projections Proximal normal cone Intrinsic transversality Finite convergence Polyhedrons LINEAR CONVERGENCE FEASIBILITY We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality, which until now has been restricted to sets with nonempty intersection. In the special case of a polyhedron and closed half space, our sufficient conditions define the minimum distance between the two sets that is required for alternating projections to converge in a single iteration. 2021 Journal Article http://hdl.handle.net/20.500.11937/89492 10.1016/j.orl.2021.04.009 English http://purl.org/au-research/grants/arc/IC180100030 ELSEVIER fulltext
spellingShingle Science & Technology
Technology
Operations Research & Management Science
Alternating projections
Proximal normal cone
Intrinsic transversality
Finite convergence
Polyhedrons
LINEAR CONVERGENCE
FEASIBILITY
Bui, Hoa
Loxton, Ryan
Moeini, A.
A note on the finite convergence of alternating projections
title A note on the finite convergence of alternating projections
title_full A note on the finite convergence of alternating projections
title_fullStr A note on the finite convergence of alternating projections
title_full_unstemmed A note on the finite convergence of alternating projections
title_short A note on the finite convergence of alternating projections
title_sort note on the finite convergence of alternating projections
topic Science & Technology
Technology
Operations Research & Management Science
Alternating projections
Proximal normal cone
Intrinsic transversality
Finite convergence
Polyhedrons
LINEAR CONVERGENCE
FEASIBILITY
url http://purl.org/au-research/grants/arc/IC180100030
http://hdl.handle.net/20.500.11937/89492