Properties of Fixed Points of Generalised Extra Gradient Methods Applied to Min-Max Problems

Amir Ali Farzin, Yuen-Man Pun, Philipp Braun, Iman Shames
4/3/2025
math.OCcs.AImath.NA

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Abstract

This paper studies properties of fixed points of generalised Extra-gradient (GEG) algorithms applied to min-max problems. We discuss connections between saddle points of the objective function of the min-max problem and GEG fixed points. We show that, under appropriate step-size selections, the set of saddle points (Nash equilibria) is a subset of stable fixed points of GEG. Convergence properties of the GEG algorithm are obtained through a stability analysis of a discrete-time dynamical system. The results and benefits when compared to existing methods are illustrated through numerical examples.

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Cite this paper

@article{farzin2025properties,
  title  = {Properties of Fixed Points of Generalised Extra Gradient Methods Applied to Min-Max Problems},
  author = {Amir Ali Farzin and Yuen-Man Pun and Philipp Braun and Iman Shames},
  year   = {2025},
  eprint = {2504.03069},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2504.03069v1}
}

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