{"ID":2839784,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.14050","arxiv_id":"2511.14050","title":"Nonlinear three-operator splitting algorithms with momentum for monotone inclusions","abstract":"In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each proposed method extends one of the classical schemes: the semi-forward-reflected-backward splitting algorithm, the semi-reflected-forward-backward splitting algorithm, and the outer reflected forward-backward splitting algorithm by incorporating a nonlinear momentum term. Under appropriate step-size conditions, we establish the weak convergence of all three algorithms, and further prove their $R$-linear convergence rates under strong monotonicity assumptions. Preliminary numerical experiments on both synthetic datasets and real-world quadratic programming problems in portfolio optimization demonstrate the effectiveness and superiority of the proposed algorithms.","short_abstract":"In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each proposed method extends one of the classical schemes: the semi-forward-reflecte...","url_abs":"https://arxiv.org/abs/2511.14050","url_pdf":"https://arxiv.org/pdf/2511.14050v1","authors":"[\"Liqian Qin\",\"Aviv Gibali\",\"Cuijie Zhang\",\"Yuchao Tang\"]","published":"2025-11-18T02:01:48Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}