Convergence of proximal splitting algorithms in CAT(κ) spaces and beyond
In the setting of CAT ( κ ) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessar...
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| Veröffentlicht in: | Fixed point theory and algorithms for sciences and engineering 2021-12, Vol.2021 (1) |
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| container_title | Fixed point theory and algorithms for sciences and engineering |
| container_volume | 2021 |
| creator | Lauster, Florian Luke, D. Russell |
| description | In the setting of
CAT
(
κ
)
spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in
p
-uniformly convex spaces. |
| doi_str_mv | 10.1186/s13663-021-00698-0 |
| format | Article |
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CAT
(
κ
)
spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in
p
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CAT
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κ
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p
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p
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| fulltext | fulltext |
| identifier | EISSN: 2730-5422 |
| ispartof | Fixed point theory and algorithms for sciences and engineering, 2021-12, Vol.2021 (1) |
| issn | 2730-5422 |
| language | eng |
| recordid | cdi_proquest_journals_2563933286 |
| source | DOAJ Directory of Open Access Journals; SpringerLink Journals - AutoHoldings; Springer Nature OA Free Journals |
| subjects | Algorithms Analysis Applications of Mathematics Convergence Differential Geometry Mathematical and Computational Biology Mathematics Mathematics and Statistics Neighborhoods Optimization and Real World Applications Topology |
| title | Convergence of proximal splitting algorithms in CAT(κ) spaces and beyond |
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