Characterization of Local Convergence for Min-max Saddle Point Problems

In this project paper, we review the convergence properties of iterations designed for the min-max saddle point problem, by revisiting and extending the classic results raised by Prof. Yin Zhang 20 years ago [9]. We give necessary and sufficient conditions for a stationary point to be a point of strong attraction in the iteration process. This concept not simply gives interpretations of the convergence behaviors certain types of algorithms in the literature, but also motivates the new design of heuristics that may outperform the current state-of-the-art algorithms.