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

Zimmermann, Jan and Tatarenko, Tatiana and Willert, Volker and Adamy, Jürgen (2021):
Projected Push-Sum Gradient Descent-Ascent for Convex Optimization with Application to Economic Dispatch Problems. (Postprint)
In: 2020 59th IEEE Conference on Decision and Control (CDC),
New York, NY, IEEE, 2020 59th IEEE Conference on Decision and Control (CDC), Jeju, 14.-18.12.2020, DOI: 10.26083/tuprints-00017573,
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Item Type: Conference or Workshop Item
Status: Postprint
Title: Projected Push-Sum Gradient Descent-Ascent for Convex Optimization with Application to Economic Dispatch Problems
Language: English
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.

Journal or Publication Title: Proceedings of the IEEE Conference on Decision & Control
Title of Book: 2020 59th IEEE Conference on Decision and Control (CDC)
Journal volume: 59
Place of Publication: New York, NY
Publisher: IEEE
Collation: 8 Seiten
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Methods and Robotics
Event Title: 2020 59th IEEE Conference on Decision and Control (CDC)
Event Location: Jeju
Event Dates: 14.-18.12.2020
Date Deposited: 23 Mar 2021 08:14
Last Modified: 23 Mar 2021 08:14
DOI: 10.26083/tuprints-00017573
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-175739
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/17573
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