Linear convergence of relocated fixed-point iterations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909962855251968 |
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| author | Atenas, Felipe Simi, Farhana Ahmed Tam, Matthew K |
| author_facet | Atenas, Felipe Simi, Farhana Ahmed Tam, Matthew K |
| contents | We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the algorithmic operator is a contraction. As a key application of our framework, we obtain linear convergence of the relocated Douglas--Rachford algorithm for finding a zero in the sum of two monotone operators in a setting with Lipschitz continuity and strong monotonicity assumptions. We also apply the framework to deduce linear convergence of variable stepsize resolvent splitting algorithms for multioperator monotone inclusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear convergence of relocated fixed-point iterations Atenas, Felipe Simi, Farhana Ahmed Tam, Matthew K Optimization and Control 47H04, 47H05, 47H09, 65K10 We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the algorithmic operator is a contraction. As a key application of our framework, we obtain linear convergence of the relocated Douglas--Rachford algorithm for finding a zero in the sum of two monotone operators in a setting with Lipschitz continuity and strong monotonicity assumptions. We also apply the framework to deduce linear convergence of variable stepsize resolvent splitting algorithms for multioperator monotone inclusions. |
| title | Linear convergence of relocated fixed-point iterations |
| topic | Optimization and Control 47H04, 47H05, 47H09, 65K10 |
| url | https://arxiv.org/abs/2512.12954 |