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On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients

On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients
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Year:    2018

Author:    Wanfang Shen, Liang Ge

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1611-m2016-0676

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 2 : pp. 183–201

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

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

Author Details

Wanfang Shen

Liang Ge

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