Trilevel and Multilevel Optimization using Monotone Operator Theory
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916224962658304 |
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| author | Shafiei, Allahkaram Kungurtsev, Vyacheslav Marecek, Jakub |
| author_facet | Shafiei, Allahkaram Kungurtsev, Vyacheslav Marecek, Jakub |
| contents | We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term.~Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_09407 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Trilevel and Multilevel Optimization using Monotone Operator Theory Shafiei, Allahkaram Kungurtsev, Vyacheslav Marecek, Jakub Optimization and Control Artificial Intelligence We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term.~Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. |
| title | Trilevel and Multilevel Optimization using Monotone Operator Theory |
| topic | Optimization and Control Artificial Intelligence |
| url | https://arxiv.org/abs/2105.09407 |