Zhou, Xu; Ma, Zhongjing; Zou, Suli; Margellos, Kostas; (2024) Distributed Momentum Based Multi-Agent Optimization with Different Constraint Sets. IEEE Transactions on Automatic Control 10.1109/tac.2024.3445575. (In press).

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Abstract

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−−√) in objective value is also established. Simulations on an ℓ1 -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.

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