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We propose a novel algorithm for solving convex, constrained and distributedoptimization problems defined on multi-agent-networks, where each agent hasexclusive access to a part of the global objective function. The agents areable to exchange information over a directed, weighted communication graph,which can be represented as a column-stochastic matrix. The algorithm combinesan adjusted push-sum consensus protocol for information diffusion and agradient descent-ascent on the local cost functions, providing convergence tothe optimum of their sum. We provide results on a reformulation of the push-suminto single matrix-updates and prove convergence of the proposed algorithm toan optimal solution, given standard assumptions in distributed optimization.The algorithm is applied to a distributed economic dispatch problem, in whichthe constraints can be expressed in local and global subsets.

Projected Push-Sum Gradient Descent-Ascent for Convex Optimizationwith Application to Economic Dispatch Problems