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In this paper, the distributed resource allocation optimization problem isinvestigated. The allocation decisions are made to minimize the sum of all theagents' local objective functions while satisfying both the global networkresource constraint and the local allocation feasibility constraints. Here thedata corresponding to each agent in this separable optimization problem, suchas the network resources, the local allocation feasibility constraint, and thelocal objective function, is only accessible to individual agent and cannot beshared with others, which renders new challenges in this distributedoptimization problem. Based on either projection or differentiated projection,two classes of continuous-time algorithms are proposed to solve thisdistributed optimization problem in an initialization-free and scalable manner.Thus, no re-initialization is required even if the operation environment ornetwork configuration is changed, making it possible to achieve a"plug-and-play" optimal operation of networked heterogeneous agents. Thealgorithm convergence is guaranteed for strictly convex objective functions,and the exponential convergence is proved for strongly convex functions withoutlocal constraints. Then the proposed algorithm is applied to the distributedeconomic dispatch problem in power grids, to demonstrate how it can achieve theglobal optimum in a scalable way, even when the generation cost, or systemload, or network configuration, is changing.

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Initialization-free Distributed Algorithms for Optimal Resource  Allocation with Feasibility Constraints and its Application to Economic  Dispatch of Power Systems