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A Semismooth Newton Multigrid Method for Constrained Elliptic Optimal Control Problems

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Advances in Global Optimization

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 95))

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Abstract

A multigrid scheme is proposed for solving the Schur complement linear systems arising in each Newton iteration when the semi-smooth Newton method is applied to solve control-constrained elliptic optimal control problems. Numerical experiments are performed to illustrate the high efficiency of our proposed method. Computation simulation shows that the convergence rate is quite robust as the regularization parameter approaches to zero.

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Acknowledgements

This work was supported by National Priority Research Project NPRP 4-451-2-168 funded by Qatar National Research Foundation.

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Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901, USA

    Jun Liu & Mingqing Xiao

  2. Texas A&M University at Qatar, 23874, Doha, Qatar

    Tingwen Huang

Authors
  1. Jun Liu
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  2. Tingwen Huang
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  3. Mingqing Xiao
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Corresponding author

Correspondence to Mingqing Xiao .

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Editors and Affiliations

  1. School of Science, Information Technology and Engineering, Federation University Australia, Ballarat, Victoria, Australia

    David Gao

  2. School Science, Inform., Tech. & Engg., Federation University Australia, Ballarat, Victoria, Australia

    Ning Ruan

  3. Dept. of Mathematical Sciences, Tsinghua University, Beijing, China

    Wenxun Xing

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© 2015 Springer International Publishing Switzerland

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Liu, J., Huang, T., Xiao, M. (2015). A Semismooth Newton Multigrid Method for Constrained Elliptic Optimal Control Problems. In: Gao, D., Ruan, N., Xing, W. (eds) Advances in Global Optimization. Springer Proceedings in Mathematics & Statistics, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-08377-3_39

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