ON EFFECTIVE STOCHASTIC GALERKIN FINITE ELEMENT METHOD FOR STOCHASTIC OPTIMAL CONTROL GOVERNED BY INTEGRAL-DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS

• 来源期刊: 计算数学（英文版）
• 关键词: Effective gradient algorithm Stochastic Galerkin method Optimal control problem Elliptic integro-differential equations with random coefficients
• 年，卷（期）: 2018,（2）
• 页码范围: 183-201
• 页数: 19页
• 语种: 英文
• DOI: 10.4208/jcm.1611-m2016-0676

摘要

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.