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

被引：1

作者：

Shen, Wanfang ^{[1
]}

Ge, Liang ^{[2
]}

机构：

[1] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Shandong, Peoples R China

[2] Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2018年 / 36卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Effective gradient algorithm; Stochastic Galerkin method; Optimal control problem; Elliptic integro-differential equations with random coefficients; COLLOCATION METHOD; INTEGRODIFFERENTIAL EQUATIONS; NUMERICAL-SOLUTION; APPROXIMATIONS; PDE;

D O I：

10.4208/jcm.1611-m2016-0676

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：183 / 201

页数：19

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