Learning solutions to some toy constrained optimization problems in infinite dimensional Hilbert spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911749976883200 |
|---|---|
| author | Mandal, Pinak |
| author_facet | Mandal, Pinak |
| contents | In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms on some toy problems originating in either calculus of variations or physics. We demonstrate that both methods are able to produce decent approximations for the test problems and are comparable in terms of different errors produced. Leveraging the common occurrence of the Lagrange multiplier update rule being computationally less expensive than solving subproblems in the penalty method, we achieve significant speedups in cases when the output of the constraint function is itself a function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning solutions to some toy constrained optimization problems in infinite dimensional Hilbert spaces Mandal, Pinak Optimization and Control Machine Learning In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms on some toy problems originating in either calculus of variations or physics. We demonstrate that both methods are able to produce decent approximations for the test problems and are comparable in terms of different errors produced. Leveraging the common occurrence of the Lagrange multiplier update rule being computationally less expensive than solving subproblems in the penalty method, we achieve significant speedups in cases when the output of the constraint function is itself a function. |
| title | Learning solutions to some toy constrained optimization problems in infinite dimensional Hilbert spaces |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2401.01306 |