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Volume 32, Issue 3
On Augmented Lagrangian Methods for Saddle-Point Linear Systems with Singular or Semidefinite (1, 1) Blocks

Tatiana S. Martynova

DOI: 10.4208/jcm.1401-CR7

J. Comp. Math., 32 (2014), pp. 297-305.

Published online: 2014-06

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  • Abstract

An effective algorithm for solving large saddle-point linear systems, presented by Krukier et al., is applied to the constrained optimization problems. This method is a modification of skew-Hermitian triangular splitting iteration methods. We consider the saddle-point linear systems with singular or semidefinite (1, 1) blocks. Moreover, this method is applied to precondition the GMRES. Numerical results have confirmed the effectiveness of the method and showed that the new method can produce high-quality preconditioners for the Krylov subspace methods for solving large sparse saddle-point linear systems.

  • Keywords

Hermitian and skew-Hermitian splitting, Saddle-point linear system, Constrained optimization, Krylov subspace method.

  • AMS Subject Headings

65F10, 65F50.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-32-297, author = {Tatiana S. Martynova}, title = {On Augmented Lagrangian Methods for Saddle-Point Linear Systems with Singular or Semidefinite (1, 1) Blocks}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {3}, pages = {297--305}, abstract = {

An effective algorithm for solving large saddle-point linear systems, presented by Krukier et al., is applied to the constrained optimization problems. This method is a modification of skew-Hermitian triangular splitting iteration methods. We consider the saddle-point linear systems with singular or semidefinite (1, 1) blocks. Moreover, this method is applied to precondition the GMRES. Numerical results have confirmed the effectiveness of the method and showed that the new method can produce high-quality preconditioners for the Krylov subspace methods for solving large sparse saddle-point linear systems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-CR7}, url = {http://global-sci.org/intro/article_detail/jcm/9887.html} }
TY - JOUR T1 - On Augmented Lagrangian Methods for Saddle-Point Linear Systems with Singular or Semidefinite (1, 1) Blocks AU - Tatiana S. Martynova JO - Journal of Computational Mathematics VL - 3 SP - 297 EP - 305 PY - 2014 DA - 2014/06 SN - 32 DO - http://doi.org/10.4208/jcm.1401-CR7 UR - https://global-sci.org/intro/article_detail/jcm/9887.html KW - Hermitian and skew-Hermitian splitting, Saddle-point linear system, Constrained optimization, Krylov subspace method. AB -

An effective algorithm for solving large saddle-point linear systems, presented by Krukier et al., is applied to the constrained optimization problems. This method is a modification of skew-Hermitian triangular splitting iteration methods. We consider the saddle-point linear systems with singular or semidefinite (1, 1) blocks. Moreover, this method is applied to precondition the GMRES. Numerical results have confirmed the effectiveness of the method and showed that the new method can produce high-quality preconditioners for the Krylov subspace methods for solving large sparse saddle-point linear systems.

Tatiana S. Martynova. (2014). On Augmented Lagrangian Methods for Saddle-Point Linear Systems with Singular or Semidefinite (1, 1) Blocks. Journal of Computational Mathematics. 32 (3). 297-305. doi:10.4208/jcm.1401-CR7
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