Linear convergence in time-varying generalized Nash equilibrium problems

Mattia Bianchi, Emilio Benenati, Sergio Grammatico
4/19/2023
math.OCcs.GTcs.MA

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Abstract

We study generalized games with full row rank equality 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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Cite this paper

@article{bianchi2023linear,
  title  = {Linear convergence in time-varying generalized Nash equilibrium problems},
  author = {Mattia Bianchi and Emilio Benenati and Sergio Grammatico},
  year   = {2023},
  eprint = {2304.09593},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2304.09593v1}
}

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