论文标题
通过自适应正则化加速安德森加速的非单身全球化
Nonmonotone Globalization for Anderson Acceleration via Adaptive Regularization
论文作者
论文摘要
安德森加速度（AA）是加速固定点迭代的一种流行方法，但可能会遭受不稳定和停滞状态。我们为AA提出了一种全球化方法，以提高稳定性并实现统一的全球和局部融合。与现有的AA全球化方法依赖于保护操作并可能阻碍局部融合的快速融合，我们采用了非单调信任区域框架，并引入了适应性二次正规化以及量身定制的接受机制。我们证明了全球融合，并表明我们的算法在适当的假设下达到了与AA相同的局部收敛。在几个数值实验中证明了我们方法的有效性。
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.
