Asymptotic behavior of penalty dynamics for constrained variational inequalities
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916860088287232 |
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| author | Qu, Siqi Staudigl, Mathias Peypouquet, Juan |
| author_facet | Qu, Siqi Staudigl, Mathias Peypouquet, Juan |
| contents | We propose a comprehensive framework for solving constrained variational inequalities via various classes of evolution equations displaying multi-scale aspects. In an infinite-dimensional Hilbertian framework, the class of dynamical systems we propose combine Tikhonov regularization and exterior penalization terms in order to induce strong convergence of trajectories to least norm solutions in the constrained domain. Our construction thus unifies the literature on regularization methods and penalty-based dynamical systems. An extension to a full splitting formulation of the constrained domain is also provided, with associated weak convergence results involving the Attouch-Czarnecki condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of penalty dynamics for constrained variational inequalities Qu, Siqi Staudigl, Mathias Peypouquet, Juan Optimization and Control We propose a comprehensive framework for solving constrained variational inequalities via various classes of evolution equations displaying multi-scale aspects. In an infinite-dimensional Hilbertian framework, the class of dynamical systems we propose combine Tikhonov regularization and exterior penalization terms in order to induce strong convergence of trajectories to least norm solutions in the constrained domain. Our construction thus unifies the literature on regularization methods and penalty-based dynamical systems. An extension to a full splitting formulation of the constrained domain is also provided, with associated weak convergence results involving the Attouch-Czarnecki condition. |
| title | Asymptotic behavior of penalty dynamics for constrained variational inequalities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.03902 |