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

作     者：Wanfang Shen Liang Ge 

作者机构：School of Mathematic and Quantitative Economics Shandong University of Finance and Economics Jinan Shandong 250014 China School of Mathematical Sciences University of Jinan Jinan Shandong 250022 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2018年第36卷第2期

页      面：183-201页

核心收录：

学科分类：080804[工学-电力电子与电力传动] 0711[理学-系统科学] 080805[工学-电工理论与新技术] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：This work was supported by National Natural Science Foundation of China (No. 11501326) 

主　　题：Effective gradient algorithm Stochastic Galerkin method Optimal controlproblem Elliptic integro-differential equations with random coefficients. 

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.