当前位置: X-MOL 学术SIAM J. Sci. Comput. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2021-03-15 , DOI: 10.1137/19m1291753
Daniela di Serafino , Dominique Orban

SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1001-A1026, January 2021.
We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semidefinite on an appropriate subspace, Dollar et al. [SIAM J. Matrix Anal. Appl., 28 (2006), pp. 170--189] describe how to apply the conjugate gradient (CG) method coupled with a constraint preconditioner, a choice that has proved to be effective in optimization applications. We investigate the design of constraint-preconditioned variants of other Krylov methods for regularized systems by focusing on the underlying basis-generation process. We build upon principles laid out by Gould, Orban, and Rees [SIAM J. Matrix Anal. Appl., 35 (2014), pp. 1329--1343] to provide general guidelines that allow us to specialize any Krylov method to regularized saddle-point systems. In particular, we obtain constraint-preconditioned variants of Lanczos and Arnoldi-based methods, including the Lanczos version of CG, MINRES, SYMMLQ, GMRES($\ell$), and DQGMRES. We also provide MATLAB implementations in hopes that they are useful as a basis for the development of more sophisticated software. Finally, we illustrate the numerical behavior of constraint-preconditioned Krylov solvers using symmetric and nonsymmetric systems arising from constrained optimization.


中文翻译:

约束预处理的Krylov求解器,用于正则化鞍点系统

SIAM科学计算杂志,第43卷,第2期,第A1001-A1026页,2021年1月。
我们考虑正则化鞍点系统的迭代解。当前导块在适当的子空间上是对称且正半定的时,Dollar等人。[SIAM J.矩阵肛门。Appl。,28(2006),pp。170--189]描述了如何应用结合了约束条件预处理器的共轭梯度(CG)方法,这一选择已被证明在优化应用中是有效的。通过关注基础生成过程,我们研究了其他Krylov方法的正则化系统的约束预处理变体的设计。我们以Gould,Orban和Rees [SIAM J. Matrix Anal。Appl。,35(2014),pp。1329--1343]中提供一般性准则,使我们可以将任何Krylov方法专门用于正则化的鞍点系统。尤其是,我们获得基于Lanczos和Arnoldi的方法的约束条件预处理的变体,包括CG,MINRES,SYMMLQ,GMRES($ \ ell $)和DQGMRES的Lanczos版本。我们还提供了MATLAB实现,希望它们可以作为开发更复杂软件的基础。最后,我们通过约束优化说明了使用对称和非对称系统进行约束预处理的Krylov求解器的数值行为。
更新日期:2021-03-16
down
wechat
bug