Trilevel and Multilevel Optimization using Monotone Operator Theory
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 lo...
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| Published in | arXiv.org |
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| Main Authors | , , |
| Format | Paper Journal Article |
| Language | English |
| Published |
Ithaca
Cornell University Library, arXiv.org
19.10.2023
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| Online Access | Get full text |
| ISSN | 2331-8422 |
| DOI | 10.48550/arxiv.2105.09407 |
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| Abstract | 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. |
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| AbstractList | Mathematical Methods of Operations Research, 2024 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. 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. |
| Author | Marecek, Jakub Kungurtsev, Vyacheslav Shafiei, Allahkaram |
| Author_xml | – sequence: 1 givenname: Allahkaram surname: Shafiei fullname: Shafiei, Allahkaram – sequence: 2 givenname: Vyacheslav surname: Kungurtsev fullname: Kungurtsev, Vyacheslav – sequence: 3 givenname: Jakub surname: Marecek fullname: Marecek, Jakub |
| BackLink | https://doi.org/10.1007/s00186-024-00852-5$$DView published paper (Access to full text may be restricted) https://doi.org/10.48550/arXiv.2105.09407$$DView paper in arXiv |
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| Copyright | 2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
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| DOI | 10.48550/arxiv.2105.09407 |
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| Snippet | We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of... Mathematical Methods of Operations Research, 2024 We consider rather a general class of multi-level optimization problems, where a convex objective function is... |
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| Title | Trilevel and Multilevel Optimization using Monotone Operator Theory |
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