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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.04934 |
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| _version_ | 1866916215567417344 |
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| author | Müller, Sebastian Petra, Stefania Zisler, Matthias |
| author_facet | Müller, Sebastian Petra, Stefania Zisler, Matthias |
| contents | We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are accurate but expensive to compute, while coarser models are less accurate but cheaper to compute. When working at the fine level, multilevel optimisation computes the search direction based on a coarser model which speeds up updates at the fine level. Moreover, exploiting geometry induced by the hierarchy the feasibility of the updates is preserved. In particular, our approach extends classical components of multigrid methods like restriction and prolongation to the Riemannian structure of our constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04934 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multilevel Geometric Optimization for Regularised Constrained Linear Inverse Problems Müller, Sebastian Petra, Stefania Zisler, Matthias Optimization and Control Computer Vision and Pattern Recognition Differential Geometry 65K10, 49J40, 49M37, 68U10, 74P20, 90C06 We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are accurate but expensive to compute, while coarser models are less accurate but cheaper to compute. When working at the fine level, multilevel optimisation computes the search direction based on a coarser model which speeds up updates at the fine level. Moreover, exploiting geometry induced by the hierarchy the feasibility of the updates is preserved. In particular, our approach extends classical components of multigrid methods like restriction and prolongation to the Riemannian structure of our constraints. |
| title | Multilevel Geometric Optimization for Regularised Constrained Linear Inverse Problems |
| topic | Optimization and Control Computer Vision and Pattern Recognition Differential Geometry 65K10, 49J40, 49M37, 68U10, 74P20, 90C06 |
| url | https://arxiv.org/abs/2207.04934 |