Non-Ergodic Convergence Algorithms for Distributed Consensus and Coupling-Constrained Optimization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917102058733568 |
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| author | Qiu, Chenyang Lin, Zongli |
| author_facet | Qiu, Chenyang Lin, Zongli |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Ergodic Convergence Algorithms for Distributed Consensus and Coupling-Constrained Optimization Qiu, Chenyang Lin, Zongli Optimization and Control Multiagent Systems Systems and Control 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. |
| title | Non-Ergodic Convergence Algorithms for Distributed Consensus and Coupling-Constrained Optimization |
| topic | Optimization and Control Multiagent Systems Systems and Control |
| url | https://arxiv.org/abs/2511.19714 |