Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems

Mattia Bianchi; Emilio Benenati; Sergio Grammatico

doi:10.1109/CDC49753.2023.10383331

Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems

Mattia Bianchi, Emilio Benenati, Sergio Grammatico

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

Abstract

We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

Original language	English
Title of host publication	Proceedings of the 62nd IEEE Conference on Decision and Control (CDC 2023)
Publisher	IEEE
Pages	7220-7226
Number of pages	7
ISBN (Electronic)	979-8-3503-0124-3
DOIs	https://doi.org/10.1109/CDC49753.2023.10383331
Publication status	Published - 2023
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023

Publication series

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

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Country/Territory	Singapore
City	Singapore
Period	13/12/23 → 15/12/23

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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10.1109/CDC49753.2023.10383331

Cite this

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title = "Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems",

abstract = "We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.",

author = "Mattia Bianchi and Emilio Benenati and Sergio Grammatico",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.; 62nd IEEE Conference on Decision and Control, CDC 2023 ; Conference date: 13-12-2023 Through 15-12-2023",

year = "2023",

doi = "10.1109/CDC49753.2023.10383331",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "IEEE",

pages = "7220--7226",

booktitle = "Proceedings of the 62nd IEEE Conference on Decision and Control (CDC 2023)",

address = "United States",

}

Bianchi, M, Benenati, E & Grammatico, S 2023, Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems. in Proceedings of the 62nd IEEE Conference on Decision and Control (CDC 2023). Proceedings of the IEEE Conference on Decision and Control, IEEE, pp. 7220-7226, 62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, 13/12/23. https://doi.org/10.1109/CDC49753.2023.10383331

Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems. / Bianchi, Mattia; Benenati, Emilio ; Grammatico, Sergio.
Proceedings of the 62nd IEEE Conference on Decision and Control (CDC 2023). IEEE, 2023. p. 7220-7226 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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T1 - Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems

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N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2023

Y1 - 2023

N2 - We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

AB - We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

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M3 - Conference contribution

AN - SCOPUS:85181706796

T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - Proceedings of the 62nd IEEE Conference on Decision and Control (CDC 2023)

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Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems

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