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Volume 3, Issue 4
Fast Solvers of Fredholm Optimal Control Problems

Mario Annunziato & Alfio Borzì

DOI: 10.4208/nmtma.2010.m9011

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 431-448.

Published online: 2010-03

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  • Abstract

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

  • Keywords

Optimal control theory, Fredholm integral equations of second kind, iterative methods.

  • AMS Subject Headings

49K22, 65K10, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-431, author = {Mario Annunziato and Alfio Borzì}, title = {Fast Solvers of Fredholm Optimal Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {4}, pages = {431--448}, abstract = {

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.m9011}, url = {http://global-sci.org/intro/article_detail/nmtma/6007.html} }
TY - JOUR T1 - Fast Solvers of Fredholm Optimal Control Problems AU - Mario Annunziato & Alfio Borzì JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 431 EP - 448 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.m9011 UR - https://global-sci.org/intro/article_detail/nmtma/6007.html KW - Optimal control theory, Fredholm integral equations of second kind, iterative methods. AB -

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

Mario Annunziato and Alfio Borzì. (2010). Fast Solvers of Fredholm Optimal Control Problems. Numerical Mathematics: Theory, Methods and Applications. 3 (4). 431-448. doi:10.4208/nmtma.2010.m9011
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