标题： 广义外梯度法应用于极小极大问题的不动点性质 显示英文标题

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

摘要： 本文研究了广义Extra-gradient（GEG）算法应用于min-max问题时的不动点性质。我们讨论了min-max问题目标函数的鞍点与GEG不动点之间的联系。我们证明，在适当的步长选择下，鞍点（纳什均衡）是GEG稳定不动点的一个子集。通过离散时间动态系统的稳定性分析获得了GEG算法的收敛性质。通过数值例子展示了与现有方法相比的结果和优势。 显示英文摘要

摘要： 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.