Mini-Batch Stochastic Krasnosel'ski\uı-Mann Algorithm for Nonexpansive Fixed Point Problems
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913015781130240 |
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| author | Iiduka, Hideaki |
| author_facet | Iiduka, Hideaki |
| contents | The Krasnosel'ski\uı-Mann algorithm is a well-known method for finding fixed points of a nonexpansive mapping with strong theoretical guarantees. However, there are practical large-scale problems to which this algorithm cannot be applied. Here, to resolve the issue caused by the computational difficulty of the mapping, we define a computable mini-batch stochastic mapping, which is a unbiased estimator of the nonexpansive mapping, and implement it in the Krasnosel'ski\uı-Mann algorithm. We show that the algorithm with increasing batch sizes converges almost surely to a fixed point of the nonexpansive mapping. We also perform a convergence rate analysis on the algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06909 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mini-Batch Stochastic Krasnosel'ski\uı-Mann Algorithm for Nonexpansive Fixed Point Problems Iiduka, Hideaki Optimization and Control 47J26, 65K05, 90C15 The Krasnosel'ski\uı-Mann algorithm is a well-known method for finding fixed points of a nonexpansive mapping with strong theoretical guarantees. However, there are practical large-scale problems to which this algorithm cannot be applied. Here, to resolve the issue caused by the computational difficulty of the mapping, we define a computable mini-batch stochastic mapping, which is a unbiased estimator of the nonexpansive mapping, and implement it in the Krasnosel'ski\uı-Mann algorithm. We show that the algorithm with increasing batch sizes converges almost surely to a fixed point of the nonexpansive mapping. We also perform a convergence rate analysis on the algorithm. |
| title | Mini-Batch Stochastic Krasnosel'ski\uı-Mann Algorithm for Nonexpansive Fixed Point Problems |
| topic | Optimization and Control 47J26, 65K05, 90C15 |
| url | https://arxiv.org/abs/2604.06909 |