Distributed Cutting Plane Method via Sample Point Consensus

• 成果类型: Article
• 署名作者: Zhong, Tianyi; Angeli, David
• 署名单位: Imperial College London; University of Florence
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3547567
• 发表日期: 2025
• 页码: 5499-5506
• 关键词: convergence; COSTS; Linear approximation; cost function; Lower bound; Approximation algorithms; training; linear programming; Data mining; TOPOLOGY; consensus; cutting plane; distributed optimization; multiagent network

摘要

This article considers a general setup for the constrained convex optimization problem over jointly fully connected time-varying networks. We propose a novel cutting plane-based method that embeds a proximity-based consensus scheme for solving this (potentially nonsmooth) optimization problem. The consensus mechanism allows agents to select the same sample point and therefore reconstruct the centralized cut individually. Under convexity, we prove that agents' sample points converge to the optimal set of the global problem. Numerical tests show the performance of the algorithm.