A Geometric Framework for Stochastic Iterations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917276099280896 |
|---|---|
| author | Combettes, Patrick L. Madariaga, Javier I. |
| author_facet | Combettes, Patrick L. Madariaga, Javier I. |
| contents | This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which existing solution methods can be recast and improved, and new ones can be designed. Almost sure weak, strong, and linear convergence results are established in particular for stochastic fixed point iterations, the stochastic gradient descent method, and stochastic extrapolated parallel algorithms for feasibility problems. In these areas, the proposed algorithms exceed the features and convergence guarantees of the state of the art. Numerical applications to signal and image recovery are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Geometric Framework for Stochastic Iterations Combettes, Patrick L. Madariaga, Javier I. Optimization and Control Probability This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which existing solution methods can be recast and improved, and new ones can be designed. Almost sure weak, strong, and linear convergence results are established in particular for stochastic fixed point iterations, the stochastic gradient descent method, and stochastic extrapolated parallel algorithms for feasibility problems. In these areas, the proposed algorithms exceed the features and convergence guarantees of the state of the art. Numerical applications to signal and image recovery are provided. |
| title | A Geometric Framework for Stochastic Iterations |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2504.02761 |