Comparison of reduced- and full-space algorithms for PDE-constrained optimization
Comparison of reduced- and full-space algorithms for PDE-constrained optimization
复制标题
PDE 约束优化的缩减空间和全空间算法的比较
DOI：
10.2514/6.2013-1043
复制
发表时间：
2013
影响因子：
3.9
通讯作者：
J. Alonso
中科院分区：
文献类型：
--
作者：
Jason E. Hicken;J. Alonso
pde约束优化问题通常用约空间拟牛顿算法求解。准牛顿方法对于自由度相对较小的问题是有效的，但随着问题规模的增大，其性能会下降。本文比较了两种避免了拟牛顿方法的算法缩放问题的非精确牛顿算法。这两种非精确牛顿算法通过简化空间和全空间实现来区分。数值实验表明，全空间（或单次）非精确牛顿算法通常是最有效的方法；然而，简化空间算法是一个有吸引力的折衷方案，因为它比全空间方法对现有求解器的入侵更少，同时保留了出色的算法缩放。我们还强调了在约简空间中使用非精确海森向量积的重要性。
PDE-constrained optimization problems are often solved using reduced-space quasi- Newton algorithms. Quasi-Newton methods are eective for problems with relatively few degrees of freedom, but their performance degrades as the problem size grows. In this paper, we compare two inexact-Newton algorithms that avoid the algorithmic scaling is- sues of quasi-Newton methods. The two inexact-Newton algorithms are distinguished by reduced-space and full-space implementations. Numerical experiments demonstrate that the full-space (or one-shot) inexact-Newton algorithm is typically the most ecient ap- proach; however, the reduced-space algorithm is an attractive compromise, because it requires less intrusion into existing solvers than the full-space approach while retaining excellent algorithmic scaling. We also highlight the importance of using inexact-Hessian- vector products in the reduced-space.