{"ID":2837811,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19714","arxiv_id":"2511.19714","title":"Non-Ergodic Convergence Algorithms for Distributed Consensus and Coupling-Constrained Optimization","abstract":"We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and global affine equalities. We first design a linearized method of multipliers for the consensus optimization problem. Without smoothness or strong convexity, we establish non-ergodic sublinear rates of order O(1/\\sqrt{k}) for both the objective optimality and the consensus violation. Leveraging duality, we then show that the economic dispatch problem admits a dual consensus formulation, and that applying the same algorithm to the dual economic dispatch yields non-ergodic O(1/\\sqrt{k}) decay for the error of the summation of the cost over the network and the equality-constraint residual under convexity and Slater's condition. Numerical results on the IEEE 118-bus system demonstrate faster reduction of both objective error and feasibility error relative to the state-of-the-art baselines, while the dual variables reach network-wide consensus.","short_abstract":"We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and global affine equalities. We first design a linearized method of multipliers for the consensus optimization problem. Without smoothness or strong convexity, we establish non-ergodic sublinear rates of order O(1/\\sq...","url_abs":"https://arxiv.org/abs/2511.19714","url_pdf":"https://arxiv.org/pdf/2511.19714v1","authors":"[\"Chenyang Qiu\",\"Zongli Lin\"]","published":"2025-11-24T21:24:06Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.MA\",\"eess.SY\"]","methods":"[]","has_code":false}