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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 leftdoi:10.1109/access.2021.3082537 fatcat:vvzluy3a6faendmr733ghdpxai