Nonmonotone Globalization for Anderson Acceleration via Adaptive Regularization

nderson acceleration ( ) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for to improve stability and achieve unified global and local convergence. Unlike existing globalization approaches that rely on safeguarding operations and might hinder fast local convergence, we adopt a nonmonotone trust-region framework and introduce an adaptive quadratic regularization together with a tailored acceptance mechanism. We prove global convergence and show that our algorithm attains the same local convergence as under appropriate assumptions. The effectiveness of our method is demonstrated in several numerical experiments.