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

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. Specifica...

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Bibliographic Details
Published in:	2020 European Control Conference (ECC) pp. 1117 - 1122
Main Authors:	Franci, Barbara, Grammatico, Sergio
Format:	Conference Proceeding
Language:	English
Published:	EUCA 01.05.2020
Subjects:	Convergence Cost function Games Nash equilibrium Random variables Stochastic processes Uncertainty
Online Access:	Get full text
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Summary:	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.
DOI:	10.23919/ECC51009.2020.9143966