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 - <p style="text-align: justify;">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.</p>