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Anderson acceleration (AA) is a popular method for accelerating fixed-pointiterations, but may suffer from instability and stagnation. We propose aglobalization method for AA to improve stability and achieve unified global andlocal convergence. Unlike existing AA globalization approaches that rely onsafeguarding operations and might hinder fast local convergence, we adopt anonmonotone trust-region framework and introduce an adaptive quadraticregularization together with a tailored acceptance mechanism. We prove globalconvergence and show that our algorithm attains the same local convergence asAA under appropriate assumptions. The effectiveness of our method isdemonstrated in several numerical experiments.

Nonmonotone Globalization for Anderson Acceleration via Adaptive Regularization