{"ID":2828768,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12954","arxiv_id":"2512.12954","title":"Linear convergence of relocated fixed-point iterations","abstract":"We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the algorithmic operator is a contraction. As a key application of our framework, we obtain linear convergence of the relocated Douglas--Rachford algorithm for finding a zero in the sum of two monotone operators in a setting with Lipschitz continuity and strong monotonicity assumptions. We also apply the framework to deduce linear convergence of variable stepsize resolvent splitting algorithms for multioperator monotone inclusions.","short_abstract":"We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the algorithmic operator is a contraction. As a key application of our framework, we obta...","url_abs":"https://arxiv.org/abs/2512.12954","url_pdf":"https://arxiv.org/pdf/2512.12954v1","authors":"[\"Felipe Atenas\",\"Farhana Ahmed Simi\",\"Matthew K Tam\"]","published":"2025-12-15T03:39:54Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}