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

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.

@article{farzin2025_2504.03069,
  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 },
  journal={arXiv preprint arXiv:2504.03069},
  year={ 2025 }
}