Regularization methods for solving hierarchical variational inequalities with complexity guarantees
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909982028464128 |
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| author | Cortild, Daniel Marschner, Meggie Staudigl, Mathias |
| author_facet | Cortild, Daniel Marschner, Meggie Staudigl, Mathias |
| contents | We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and equilibrium selection problems. In a real Hilbert space setting, we combine a Tikhonov regularization and a proximal penalization to develop a flexible double-loop method for which we prove asymptotic convergence and provide rate statements in terms of gap functions. Our method is flexible, and effectively accommodates a large class of structured operator splitting formulations for which fixed-point encodings are available. Finally, we validate our findings numerically on various examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_20772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularization methods for solving hierarchical variational inequalities with complexity guarantees Cortild, Daniel Marschner, Meggie Staudigl, Mathias Optimization and Control 90C33 We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and equilibrium selection problems. In a real Hilbert space setting, we combine a Tikhonov regularization and a proximal penalization to develop a flexible double-loop method for which we prove asymptotic convergence and provide rate statements in terms of gap functions. Our method is flexible, and effectively accommodates a large class of structured operator splitting formulations for which fixed-point encodings are available. Finally, we validate our findings numerically on various examples. |
| title | Regularization methods for solving hierarchical variational inequalities with complexity guarantees |
| topic | Optimization and Control 90C33 |
| url | https://arxiv.org/abs/2512.20772 |