  This paper introduces the Multiple Greedy Quasi-Newton (MGSR1-SP) method, a
novel approach to solving strongly-convex-strongly-concave (SCSC) saddle point
problems. Our method enhances the approximation of the squared indefinite
Hessian matrix inherent in these problems, significantly improving both
stability and efficiency through iterative greedy updates. We provide a
thorough theoretical analysis of MGSR1-SP, demonstrating its linear-quadratic
convergence rate. Numerical experiments conducted on AUC maximization and
adversarial debiasing problems, compared with state-of-the-art algorithms,
underscore our method's enhanced convergence rate. These results affirm the
potential of MGSR1-SP to improve performance across a broad spectrum of machine
learning applications where efficient and accurate Hessian approximations are
crucial.
