This paper considers a class of consensus optimization problems over a time-varying communication network wherein each agent can only interact with its neighbours. The target is to minimize the summation of all local and possibly non-smooth objectives in the presence of different constraint sets per agent. To achieve this goal, we propose a novel distributed heavy-ball algorithm that combines the subgradient tracking technique with a momentum term related to history information. This algorithm promotes the distributed application of existing centralized accelerated momentum methods, especially for constrained non-smooth problems. Under certain assumptions and conditions on the step-size and momentum coefficient, the convergence and optimality of the proposed algorithm can be guaranteed through a rigorous theoretical analysis, and a convergence rate of O(lnk/k__√)\mathcal {O}(\rm {ln}k/ \sqrt{k}) in objective value is also established. Simulations on an _1\ell _{1}-regularized logistic-regression problem show that the proposed algorithm can achieve faster convergence than existing related distributed algorithms, while a case study involving a building energy management problem further demonstrates its efficacy.

中文翻译：

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不同约束集下基于分布式动量的多智能体优化


本文考虑了时变通信网络上的一类共识优化问题，其中每个代理只能与其邻居交互。目标是在每个代理存在不同约束集的情况下最小化所有局部目标和可能的非平滑目标的总和。为了实现这一目标，我们提出了一种新颖的分布式重球算法，该算法将次梯度跟踪技术与与历史信息相关的动量项相结合。该算法促进了现有集中式加速动量方法的分布式应用，特别是对于约束非光滑问题。在步长和动量系数一定的假设和条件下，通过严格的理论分析可以保证所提算法的收敛性和最优性，收敛速度为O(lnk/k__√)\mathcal {O}(\目标值 rm {ln}k/ \sqrt{k}) 也成立。对_1\ell _{1}-正则化逻辑回归问题的模拟表明，所提出的算法比现有的相关分布式算法能够实现更快的收敛，而涉及建筑能源管理问题的案例研究进一步证明了其有效性。