{"ID":2877226,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.20872","arxiv_id":"2508.20872","title":"Tikhonov regularized exterior penalty methods for hierarchical variational inequalities","abstract":"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.","short_abstract":"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 bil...","url_abs":"https://arxiv.org/abs/2508.20872","url_pdf":"https://arxiv.org/pdf/2508.20872v1","authors":"[\"Meggie Marschner\",\"Mathias Staudigl\"]","published":"2025-08-28T15:02:19Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}