{"ID":6497644,"CreatedAt":"2026-07-13T01:19:40.13847098Z","UpdatedAt":"2026-07-14T01:36:59.12045529Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.09495","arxiv_id":"2607.09495","title":"Inertial forward-backward algorithm with exterior penalization and Tikhonov regularization","abstract":"In a real Hilbertian setting, we develop in this paper numerical splitting techniques guaranteeing strong convergence to the least norm solution of constrained variational inequalities. We develop a multiscale inertial forward-backward splitting algorithm for solving constrained monotone inclusion problems with multiscale penalization and vanishing Tikhonov regularization. The proposed framework accommodates smooth, nonsmooth, and mixed smooth--nonsmooth penalty operators, providing a unified treatment of a broad class of constrained monotone inclusion problems. In this general framework, we establish weak convergence of the generated iterates. By introducing a discrete Tikhonov central path, we further prove strong convergence to the minimum-norm solution of the problem under a mild constraint qualification condition on the problem data.","short_abstract":"In a real Hilbertian setting, we develop in this paper numerical splitting techniques guaranteeing strong convergence to the least norm solution of constrained variational inequalities. We develop a multiscale inertial forward-backward splitting algorithm for solving constrained monotone inclusion problems with multisc...","url_abs":"https://arxiv.org/abs/2607.09495","url_pdf":"https://arxiv.org/pdf/2607.09495v1","authors":"[\"Siqi Qu\",\"Juan Peypouquet\",\"Mathias Staudigl\"]","published":"2026-07-10T15:08:51Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}