{"ID":2837767,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19637","arxiv_id":"2511.19637","title":"Extending Douglas-Rachford Splitting for Convex Optimization","abstract":"The Douglas-Rachford splitting method is a classical and widely used algorithm for solving monotone inclusions involving the sum of two maximally monotone operators. It was recently shown to be the unique frugal, no-lifting resolvent-splitting method that is unconditionally convergent in the general two-operator setting. In this work, we show that this uniqueness does not hold in the convex optimization case: when the operators are subdifferentials of proper, closed, convex functions, a strictly larger class of frugal, no-lifting resolvent-splitting methods is unconditionally convergent. We provide a complete characterization of all such methods in the convex optimization setting and prove that this characterization is sharp: unconditional convergence holds exactly on the identified parameter regions. These results immediately yield new families of convergent ADMM-type and Chambolle-Pock-type methods obtained through their Douglas-Rachford reformulations.","short_abstract":"The Douglas-Rachford splitting method is a classical and widely used algorithm for solving monotone inclusions involving the sum of two maximally monotone operators. It was recently shown to be the unique frugal, no-lifting resolvent-splitting method that is unconditionally convergent in the general two-operator settin...","url_abs":"https://arxiv.org/abs/2511.19637","url_pdf":"https://arxiv.org/pdf/2511.19637v2","authors":"[\"Max Nilsson\",\"Anton Åkerman\",\"Pontus Giselsson\"]","published":"2025-11-24T19:13:54Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}