Volume 13, Issue 4
A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems

Owe Axelsson & Davod Khojasteh Salkuyeh

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 1098-1122.

Published online: 2020-06

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  • Abstract

Optimal control problems constrained by a partial differential equation (PDE) arise in various important applications, such as in engineering and natural sciences. Normally the problems are of very large scale, so iterative solution methods must be used. Thereby the choice of an iteration method in conjunction with an efficient preconditioner is essential. In this paper, we consider a new iteration method and a new preconditioning technique for an elliptic PDE-constrained optimal control problem with a distributed control function. Some earlier used iteration methods and preconditioners in the literature are compared, both analytically and numerically with the new iteration method and the preconditioner.

  • Keywords

Preconditioner, hybrid, PRESB, GMRES, PDE-constrained optimization, optimization.

  • AMS Subject Headings

49M25, 49K20, 65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-13-1098, author = {Owe Axelsson , and Davod Khojasteh Salkuyeh , }, title = {A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {1098--1122}, abstract = {

Optimal control problems constrained by a partial differential equation (PDE) arise in various important applications, such as in engineering and natural sciences. Normally the problems are of very large scale, so iterative solution methods must be used. Thereby the choice of an iteration method in conjunction with an efficient preconditioner is essential. In this paper, we consider a new iteration method and a new preconditioning technique for an elliptic PDE-constrained optimal control problem with a distributed control function. Some earlier used iteration methods and preconditioners in the literature are compared, both analytically and numerically with the new iteration method and the preconditioner.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0016}, url = {http://global-sci.org/intro/article_detail/nmtma/16968.html} }
TY - JOUR T1 - A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems AU - Owe Axelsson , AU - Davod Khojasteh Salkuyeh , JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1098 EP - 1122 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2020-0016 UR - https://global-sci.org/intro/article_detail/nmtma/16968.html KW - Preconditioner, hybrid, PRESB, GMRES, PDE-constrained optimization, optimization. AB -

Optimal control problems constrained by a partial differential equation (PDE) arise in various important applications, such as in engineering and natural sciences. Normally the problems are of very large scale, so iterative solution methods must be used. Thereby the choice of an iteration method in conjunction with an efficient preconditioner is essential. In this paper, we consider a new iteration method and a new preconditioning technique for an elliptic PDE-constrained optimal control problem with a distributed control function. Some earlier used iteration methods and preconditioners in the literature are compared, both analytically and numerically with the new iteration method and the preconditioner.

Owe Axelsson & Davod Khojasteh Salkuyeh. (2020). A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 1098-1122. doi:10.4208/nmtma.OA-2020-0016
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