{"ID":6138344,"CreatedAt":"2026-07-09T01:07:32.349475501Z","UpdatedAt":"2026-07-11T15:55:22.600961252Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.07585","arxiv_id":"2607.07585","title":"Convergence Analysis of the Restarted Moving-Anchored Extra-Gradient Method in the Absence of Local Lipschitz Continuity","abstract":"In this paper, we introduce the moving-anchored extra-gradient (MAEG) method for solving monotone inclusion problems involving the sum of a continuous monotone operator and a maximal monotone operator. Notably, the distance from the anchor point to the solution set is designed to be monotonically non-increasing. Under Lipschitz continuity of the forward operator, MAEG attains an $\\mathcal{O}(1/k)$ non-asymptotic iteration complexity, and when a positive anchor-update parameter is used, it further achieves an $o(1/k)$ asymptotic rate. Furthermore, leveraging the specific behavior of the anchor point, we propose a tailored restart strategy. We demonstrate that this strategy ensures convergence even in the absence of local Lipschitz continuity, while preserving the original iteration complexity guarantees whenever the Lipschitz condition holds.","short_abstract":"In this paper, we introduce the moving-anchored extra-gradient (MAEG) method for solving monotone inclusion problems involving the sum of a continuous monotone operator and a maximal monotone operator. Notably, the distance from the anchor point to the solution set is designed to be monotonically non-increasing. Under...","url_abs":"https://arxiv.org/abs/2607.07585","url_pdf":"https://arxiv.org/pdf/2607.07585v1","authors":"[\"Defeng Sun\",\"Liping Zhang\",\"Wei Zhao\"]","published":"2026-07-08T16:07:24Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}