标题： 分布式分解算法在网络上有约束凸优化的指数收敛性 显示英文标题

标题： Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks

摘要： 我们提出了一种用于网络上约束凸优化的分而治之（DAC）算法，其中全局目标是各个代理附带的局部目标之和。 该算法是完全分布式的：每次迭代在选定的融合中心周围求解局部子问题，并仅与相邻的融合中心进行协调。 在目标函数的平滑性、强凸性和局部性的标准假设下，以及在基础图上的多项式增长条件下，我们建立了DAC迭代的指数收敛性，并推导了精确和不精确局部求解器的显式界限。 对三种代表性损失（$L_2$距离、二次项和熵）的数值实验验证了理论，并展示了可扩展性和有效性。 显示英文摘要

摘要： We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and coordinates only with neighboring fusion centers. Under standard assumptions of smoothness, strong convexity, and locality on the objective function, together with polynomial growth conditions on the underlying graph, we establish exponential convergence of the DAC iterations and derive explicit bounds for both exact and inexact local solvers. Numerical experiments on three representative losses ($L_2$ distance, quadratic, and entropy) confirm the theory and demonstrate scalability and effectiveness.