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arXiv · 2004.02854

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

Jan Zimmermann·Tatiana Tatarenko·Volker Willert·Jürgen Adamy
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Abstract

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.

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Jan Zimmermann, Tatiana Tatarenko, Volker Willert, Jürgen Adamy. 2020-04-06. Projected Push-Sum Gradient Descent-Ascent for Convex Optimizationwith Application to Economic Dispatch Problems. https://arxiv.org/abs/2004.02854

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