{"ID":2825980,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.20772","arxiv_id":"2512.20772","title":"Regularization methods for solving hierarchical variational inequalities with complexity guarantees","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.20772","url_pdf":"https://arxiv.org/pdf/2512.20772v2","authors":"[\"Daniel Cortild\",\"Meggie Marschner\",\"Mathias Staudigl\"]","published":"2025-12-23T21:19:38Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}