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