Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems
| Autor: | Dominique Orban, Daniela di Serafino |
|---|---|
| Přispěvatelé: | DI SERAFINO, Daniela, Orban, Dominique |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Regularized saddle-point systems
0211 other engineering and technologies Mathematics::Optimization and Control 02 engineering and technology 010103 numerical & computational mathematics Positive-definite matrix Krylov solvers 01 natural sciences Mathematics::Numerical Analysis regularized saddle-point systems constraint preconditioners Lanczos procedure Arnoldi procedure Krylov solvers constraint preconditioners Saddle point FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Saddle Mathematics Block (data storage) 021103 operations research Applied Mathematics 65F08 65F10 65F50 90C20 Numerical Analysis (math.NA) Matrix anal Computer Science::Numerical Analysis Lanczos and Arnoldi procedures Constraint (information theory) Computational Mathematics Computer Science::Mathematical Software Subspace topology |
| Popis: | We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) 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 (2014) 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(m) 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. Comment: Accepted for publication in the SIAM Journal on Scientific Computing |
| Databáze: | OpenAIRE |
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