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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| Format: | Journal Article |
| Language: | English |
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2021
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| Online Access: | http://purl.org/au-research/grants/arc/IC180100030 http://hdl.handle.net/20.500.11937/89492 |
| _version_ | 1848765232004988928 |
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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. |
| first_indexed | 2025-11-14T11:31:58Z |
| format | Journal Article |
| id | curtin-20.500.11937-89492 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:31:58Z |
| publishDate | 2021 |
| publisher | ELSEVIER |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |