Various distributed optimization methods have been developed for solvingproblems which have simple local constraint sets and whose objective functionis the sum of local cost functions of distributed agents in a network.Motivated by emerging applications in smart grid and distributed sparseregression, this paper studies distributed optimization methods for solvinggeneral problems which have a coupled global cost function and have inequalityconstraints. We consider a network scenario where each agent has no globalknowledge and can access only its local mapping and constraint functions. Tosolve this problem in a distributed manner, we propose a consensus-baseddistributed primal-dual perturbation (PDP) algorithm. In the algorithm, agentsemploy the average consensus technique to estimate the global cost andconstraint functions via exchanging messages with neighbors, and meanwhile usea local primal-dual perturbed subgradient method to approach a global optimum.The proposed PDP method not only can handle smooth inequality constraints butalso non-smooth constraints such as some sparsity promoting constraints arisingin sparse optimization. We prove that the proposed PDP algorithm converges toan optimal primal-dual solution of the original problem, under standard problemand network assumptions. Numerical results illustrating the performance of theproposed algorithm for a distributed demand response control problem in smartgrid are also presented.
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