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Distributed Primal-Dual Perturbation Algorithm Over Unbalanced Directed Networks

This paper investigates a primal-dual method for a convex optimization problem that has coupled inequality constraints. A group of agents searches for an optimal solution over unbalanced directed communication networks by a consensus-based perturbation algorithm. Each agent computes perturbation points for the estimation of a saddle point of a Lagrange function. The primal and dual variables are updated based on a gradient-based algorithm. In addition, each agent estimates a normalized left eigenvector of a weight matrix for the communication graph in order to compensate for unbalanced directed communication flows. The convergence properties of the proposed primal-dual perturbation algorithm are shown based on the row stochasticity of the weight matrix. The application of the proposed method is also considered for a distributed economic dispatch problem.