A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games

Giuseppe Belgioioso; Sergio Grammatico

doi:10.1109/CDC.2018.8619610

A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games

Giuseppe Belgioioso, Sergio Grammatico

Control Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

14 Citations (Scopus)

Abstract

We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	3541-3546
Number of pages	6
ISBN (Electronic)	978-1-5386-1395-5
DOIs	https://doi.org/10.1109/CDC.2018.8619610
Publication status	Published - 18 Jan 2019
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018 Conference number: 57

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Abbreviated title	CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

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10.1109/CDC.2018.8619610

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Belgioioso, G., & Grammatico, S. (2019). A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 3541-3546). [8619610] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2018.8619610

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abstract = "We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.",

author = "Giuseppe Belgioioso and Sergio Grammatico",

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doi = "10.1109/CDC.2018.8619610",

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Belgioioso, G & Grammatico, S 2019, A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619610, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers, Piscataway, pp. 3541-3546, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, Florida, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619610

A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games. / Belgioioso, Giuseppe; Grammatico, Sergio.

2018 IEEE Conference on Decision and Control, CDC 2018. Piscataway : Institute of Electrical and Electronics Engineers, 2019. p. 3541-3546 8619610 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.

AB - We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.

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Belgioioso G, Grammatico S. A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games. In 2018 IEEE Conference on Decision and Control, CDC 2018. Piscataway: Institute of Electrical and Electronics Engineers. 2019. p. 3541-3546. 8619610. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2018.8619610

A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games

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