{"ID":2849156,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.24489","arxiv_id":"2510.24489","title":"Nonlinear forward-backward-half forward splitting with momentum for monotone inclusions","abstract":"In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method augments the forward-backward-half forward splitting algorithm with a nonlinear momentum term. Under appropriate conditions on the step-size, we prove the weak convergence of the proposed algorithm. A linear convergence rate is also obtained under the strong monotonicity assumption. Furthermore, we investigate a stochastic variance-reduced forward-backward-half forward splitting algorithm with momentum for solving finite-sum monotone inclusion problems. Weak almost sure convergence and linear convergence are also established under standard condition. Preliminary numerical experiments on synthetic datasets and real-world quadratic programming problems in portfolio optimization demonstrate the effectiveness and superiority of the proposed algorithm.","short_abstract":"In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method augments the forward-backward-half forward splitting algorithm with a nonlinear mo...","url_abs":"https://arxiv.org/abs/2510.24489","url_pdf":"https://arxiv.org/pdf/2510.24489v2","authors":"[\"Liqian Qin\",\"Yuchao Tang\",\"Jigen Peng\"]","published":"2025-10-28T15:04:40Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}