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

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Abstract

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.

Original languageEnglish
Pages (from-to)5467-5473
JournalIEEE Transactions on Automatic Control
Volume66
Issue number11
DOIs
Publication statusPublished - 2021

Bibliographical note

Accepted Author Manuscript

Keywords

  • Approximation algorithms
  • Convergence
  • Cost function
  • Nash equilibrium
  • Random variables
  • stochastic approximation
  • Stochastic generalized Nash equilibrium problems
  • Stochastic processes
  • Uncertainty
  • variational inequalities

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