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A collection of optimization problems central to power system operation requires distributed solution architectures to avoid the need for aggregation of all information at a central location. In this paper, we study distributed dual subgradient methods to solve three such optimization problems. Namely, these are tie-line scheduling in multi-area power systems, coordination of distributed energy resources in radial distribution networks, and joint dispatch of transmission and distribution assets. With suitable relaxations or approximations of the power flow equations, all three problems can be reduced to a multi-agent constrained convex optimization problem. We utilize a constant step-size dual subgradient method with averaging on these problems. For this algorithm, we provide a convergence guarantee that is shown to be order-optimal. We illustrate its application on the grid optimization problems.
This paper studies the distributed optimization problem where the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact subgradients of th
Dual decomposition is widely utilized in distributed optimization of multi-agent systems. In practice, the dual decomposition algorithm is desired to admit an asynchronous implementation due to imperfect communication, such as time delay and packet d
Considering the constrained stochastic optimization problem over a time-varying random network, where the agents are to collectively minimize a sum of objective functions subject to a common constraint set, we investigate asymptotic properties of a d
Optimization in distributed networks plays a central role in almost all distributed machine learning problems. In principle, the use of distributed task allocation has reduced the computational time, allowing better response rates and higher data rel
Distributed optimization is concerned with using local computation and communication to realize a global aim of optimizing the sum of local objective functions. It has gained wide attention for a variety of applications in networked systems. This pap