Nonmonotone Globalization for Anderson Acceleration via Adaptive Regularization
arXiv:2006.02559
Abstract
Anderson acceleration (AA) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for AA to improve stability and achieve unified global and local convergence. Unlike existing AA 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 AA under appropriate assumptions. The effectiveness of our method is demonstrated in several numerical experiments.
Accepted to Journal of Scientific Computing
References in corpus (5)
- Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media
- Anderson Accelerated Douglas-Rachford Splitting
- Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations
- Anderson Acceleration of Proximal Gradient Methods
- Anderson Acceleration for Reinforcement Learning