Multiple Scale Methods For Optimization Of Discretized Continuous Functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912940979912704 |
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| author | Richardson, Nicholas J. E. Marusenko, Noah Friedlander, Michael P. |
| author_facet | Richardson, Nicholas J. E. Marusenko, Noah Friedlander, Michael P. |
| contents | A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on progressively finer grids. Greedy and lazy variants are analyzed and convergence guarantees are derived that show the multiscale approach achieves provably tighter error bounds at lower computational cost than single-scale optimization. The analysis extends to any base algorithm with iterate convergence at a fixed rate. Constraint modification techniques preserve feasibility across scales. Numerical experiments on probability density estimation problems, including geological data, demonstrate speedups of an order of magnitude or better. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13993 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple Scale Methods For Optimization Of Discretized Continuous Functions Richardson, Nicholas J. E. Marusenko, Noah Friedlander, Michael P. Numerical Analysis Optimization and Control 65B99, 65D15, 90C59 A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on progressively finer grids. Greedy and lazy variants are analyzed and convergence guarantees are derived that show the multiscale approach achieves provably tighter error bounds at lower computational cost than single-scale optimization. The analysis extends to any base algorithm with iterate convergence at a fixed rate. Constraint modification techniques preserve feasibility across scales. Numerical experiments on probability density estimation problems, including geological data, demonstrate speedups of an order of magnitude or better. |
| title | Multiple Scale Methods For Optimization Of Discretized Continuous Functions |
| topic | Numerical Analysis Optimization and Control 65B99, 65D15, 90C59 |
| url | https://arxiv.org/abs/2512.13993 |