A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking

Barbara Franci; Sergio Grammatico

doi:10.23919/ECC51009.2020.9143966

A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking

Barbara Franci
, Sergio Grammatico

Team Bart De Schutter

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

9 Citations (Scopus)

Abstract

We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward- backward operator splitting and a suitable preconditioning matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.

Original language	English
Title of host publication	Proceedings of the European Control Conference 2020, ECC 2020
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	1117-1122
ISBN (Electronic)	978-3-907144-01-5
ISBN (Print)	978-3-907144-02-2
DOIs	https://doi.org/10.23919/ECC51009.2020.9143966
Publication status	Published - 2020
Event	18th European Control Conference, ECC 2020 - Saint Petersburg, Russia Duration: 12 May 2020 → 15 May 2020

Conference

Conference	18th European Control Conference, ECC 2020
Country/Territory	Russia
City	Saint Petersburg
Period	12/05/20 → 15/05/20

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10.23919/ECC51009.2020.9143966

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title = "A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking",

abstract = "We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward- backward operator splitting and a suitable preconditioning matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.",

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AU - Franci, Barbara

AU - Grammatico, Sergio

PY - 2020

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N2 - We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward- backward operator splitting and a suitable preconditioning matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.

AB - We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward- backward operator splitting and a suitable preconditioning matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.

UR - https://www.scopus.com/pages/publications/85090143416

U2 - 10.23919/ECC51009.2020.9143966

DO - 10.23919/ECC51009.2020.9143966

M3 - Conference contribution

AN - SCOPUS:85090143416

SN - 978-3-907144-02-2

SP - 1117

EP - 1122

BT - Proceedings of the European Control Conference 2020, ECC 2020

PB - IEEE

CY - Piscataway, NJ, USA

T2 - 18th European Control Conference, ECC 2020

Y2 - 12 May 2020 through 15 May 2020

ER -

A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking

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