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

Giuseppe Belgioioso, Sergio Grammatico

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (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.

LanguageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages3541-3546
Number of pages6
ISBN (Electronic)978-1-5386-1395-5
DOIs
StatePublished - 18 Jan 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: 17 Dec 201819 Dec 2018
Conference number: 57

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
Abbreviated titleCDC 2018
CountryUnited States
CityMiami
Period17/12/1819/12/18

Fingerprint

Generalized Game
Decentralized
Game
Monotone
Forward-backward Algorithm
Operator Theory
Equilibrium Problem
Global Convergence
Resource Allocation
Resource allocation
Inclusion
Zero
Operator

Cite this

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] Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.1109/CDC.2018.8619610
Belgioioso, Giuseppe ; Grammatico, Sergio. / A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games. 2018 IEEE Conference on Decision and Control, CDC 2018. Piscataway : Institute of Electrical and Electronics Engineers, 2019. pp. 3541-3546
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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, Institute of Electrical and Electronics Engineers, Piscataway, pp. 3541-3546, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. DOI: 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.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-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.

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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. Available from, DOI: 10.1109/CDC.2018.8619610