Tikhonov regularized exterior penalty methods for hierarchical variational inequalities
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911127860936704 |
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| author | Marschner, Meggie Staudigl, Mathias |
| author_facet | Marschner, Meggie Staudigl, Mathias |
| contents | We consider nested variational inequalities con- sisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. This class of hierarchical equilibrium contains a wealth of important applications, including purely hierarchical convex bilevel optimization problems and certain multi-follower games. Working within a real Hilbert space setting, we develop a double loop prox-penalization algorithm with strong conver- gence guarantees towards a solution of the nested VI problem. We present various application that fit into our framework and present also some preliminary numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tikhonov regularized exterior penalty methods for hierarchical variational inequalities Marschner, Meggie Staudigl, Mathias Optimization and Control We consider nested variational inequalities con- sisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. This class of hierarchical equilibrium contains a wealth of important applications, including purely hierarchical convex bilevel optimization problems and certain multi-follower games. Working within a real Hilbert space setting, we develop a double loop prox-penalization algorithm with strong conver- gence guarantees towards a solution of the nested VI problem. We present various application that fit into our framework and present also some preliminary numerical results. |
| title | Tikhonov regularized exterior penalty methods for hierarchical variational inequalities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.20872 |