@Article{JCM-36-2,
author = {Wanfang, Shen and Liang, Ge},
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 = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1611-m2016-0676},
url = {https://global-sci.com/article/84462/on-effective-stochastic-galerkin-finite-element-method-for-stochastic-optimal-control-governed-by-integral-differential-equations-with-random-coefficients}
}