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Volume 36, Issue 2
On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients

Wanfang Shen & Liang Ge

DOI: 10.4208/jcm.1611-m2016-0676

J. Comp. Math., 36 (2018), pp. 183-201.

Published online: 2018-04

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  • Abstract

In this paper, we apply stochastic Galerkin finite element methods to the optimal control problem governed by an elliptic integral-differential PDEs with random field. The control problem has the control constraints of obstacle type. A new gradient algorithm based on the pre-conditioner conjugate gradient algorithm (PCG) is developed for this optimal control problem. This algorithm can transform a part of the state equation matrix and co-state equation matrix into block diagonal matrix and then solve the optimal control systems iteratively. The proof of convergence for this algorithm is also discussed. Finally numerical examples of a medial size are presented to illustrate our theoretical results.

  • Keywords

Effective gradient algorithm, Stochastic Galerkin method, Optimal control problem, Elliptic integro-differential equations with random coefficients.

  • AMS Subject Headings

65N06, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wfshen@sdufe.edu.cn (Wanfang Shen)

gel@sdas.org (Liang Ge)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-183, author = {Shen , Wanfang and Ge , Liang}, title = {On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {2}, pages = {183--201}, abstract = {

In this paper, we apply stochastic Galerkin finite element methods to the optimal control problem governed by an elliptic integral-differential PDEs with random field. The control problem has the control constraints of obstacle type. A new gradient algorithm based on the pre-conditioner conjugate gradient algorithm (PCG) is developed for this optimal control problem. This algorithm can transform a part of the state equation matrix and co-state equation matrix into block diagonal matrix and then solve the optimal control systems iteratively. The proof of convergence for this algorithm is also discussed. Finally numerical examples of a medial size are presented to illustrate our theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1611-m2016-0676}, url = {http://global-sci.org/intro/article_detail/jcm/12255.html} }
TY - JOUR T1 - On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients AU - Shen , Wanfang AU - Ge , Liang JO - Journal of Computational Mathematics VL - 2 SP - 183 EP - 201 PY - 2018 DA - 2018/04 SN - 36 DO - http://doi.org/10.4208/jcm.1611-m2016-0676 UR - https://global-sci.org/intro/article_detail/jcm/12255.html KW - Effective gradient algorithm, Stochastic Galerkin method, Optimal control problem, Elliptic integro-differential equations with random coefficients. AB -

In this paper, we apply stochastic Galerkin finite element methods to the optimal control problem governed by an elliptic integral-differential PDEs with random field. The control problem has the control constraints of obstacle type. A new gradient algorithm based on the pre-conditioner conjugate gradient algorithm (PCG) is developed for this optimal control problem. This algorithm can transform a part of the state equation matrix and co-state equation matrix into block diagonal matrix and then solve the optimal control systems iteratively. The proof of convergence for this algorithm is also discussed. Finally numerical examples of a medial size are presented to illustrate our theoretical results.

Wanfang Shen & Liang Ge. (2020). On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients. Journal of Computational Mathematics. 36 (2). 183-201. doi:10.4208/jcm.1611-m2016-0676
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