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