Distributed Momentum-Based Multiagent Optimization With Different Constraint Sets

In this article, we consider a class of consensus optimization problems over a time-varying communication network wherein each agent can only interact with its neighbors. The target is to minimize the summation of all local and possibly nonsmooth 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 nonsmooth 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\text {ln}k/ \sqrt{k})$</tex-math></inline-formula> in objective value is also established. Simulations on an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula>-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.