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• Apply relaxed ADMM method to address DERs coordination in a decentralized way. • Introduce energy storage devices with charging/discharging efficiency taken into account. • Allow possibly non-smooth cost functions of DERs. Distributed optimization algorithms contribute to an insight for the optimal coordination of distributed energy resources (DERs). To tackle the DER coordination problem, this paper studies a composite constrained optimization problem over multi-agent networks, where all agents independently maintain convex objective functions while satisfying the local and coupled constraints. Within the Peaceman-Rachford splitting (PRS) framework, a distributed algorithm based on the relaxed ADMM method is proposed for the considered problem, where agents in the network commonly share a fixed step-size instead of the diminishing one. Finally, the simulations on the optimal coordination of DERs including distributed generators (DGs) and energy storages (ESs) are conducted to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we deal with decision-coupled problems involving multiple agents over a network. Each agent has its own local objective function and local constraints, and all agents aim at finding the value of a common decision vector that minimizes the sum of all agents' cost functions and satisfies all local constraints. To this purpose, we introduce a Proximal-Tracking distributed optimization algorithm that integrates dynamic average consensus within the proximal minimization method. Convergence to an optimal consensus solution is guaranteed for any value of a constant penalty parameter, under a convexity assumption only, without requiring differentiability, Lipschitz continuity, or smoothness of the local objective functions. Numerical simulations show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a class of optimization problems is investigated, where the objective function is the sum of N convex functions viewed as local functions and the constraints are N nonidentical closed convex sets. Additionally, it is aimed to solve the considered optimization problem in a distributed manner and thus a sequence of time-varying unbalanced directed graphs is introduced first to depict the information connection topologies. Then, the novel push-sum based constrained optimization algorithm (PSCOA) is developed, where the new gradient descent-like method is applied to settle the involved closed convex set constraints. Furthermore, the rigorous convergence analysis is shown under some standard and common assumptions and it is proved that the developed distributed discrete-time algorithm owns a convergence rate of O ( ln t t ) in general case. Specially, the convergence rate of O ( 1 t ) can be further obtained under the assumption that at least one objective function is strongly convex. Finally, simulation results are given to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]