Properties of Fixed Points of Generalised Extra Gradient Methods Applied to Min-Max Problems
This work provides theoretical insights into optimization algorithms for min-max problems, but it is incremental as it builds on existing Extra-gradient methods.
The paper analyzes fixed points of generalized Extra-gradient (GEG) algorithms for min-max problems, showing that saddle points are stable fixed points under certain step-size conditions, with convergence demonstrated through stability analysis and numerical examples.
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.