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

共 50 条

[21] ON THE CONVERGENCE OF THE STOCHASTIC GALERKIN METHOD FOR RANDOM ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
Mugler, Antje
Starkloff, Hans-Joerg
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2013, 47 (05): : 1237 - 1263
[22] A Sparse Grid Stochastic Collocation Discontinuous Galerkin Method for Constrained Optimal Control Problem Governed by Random Convection Dominated Diffusion Equations
Ge, Liang
Sun, Tongjun
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2019, 40 (07) : 763 - 797
[23] Stochastic optimal control with random coefficients and associated stochastic Hamilton–Jacobi–Bellman equations
Jun Moon
Advances in Continuous and Discrete Models, 2022
[24] Finite element analysis for pseudo hyperbolic integral-differential equations
Cui, X
NUMERICAL TREATMENT OF MULTIPHASE FLOWS IN POROUS MEDIA, 2000, 552 : 104 - 115
[25] Solution of stochastic partial differential equations using Galerkin finite element techniques
Deb, MK
Babuska, IM
Oden, JT
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (48) : 6359 - 6372
[26] A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control
Gong, Benxue
Sun, Tongjun
Shen, Wanfang
Liu, Wenbin
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2016, 13 (05)
[27] Optimal Controls of Stochastic Differential Equations with Jumps and Random Coefficients: Stochastic Hamilton–Jacobi–Bellman Equations with Jumps
Qingxin Meng
Yuchao Dong
Yang Shen
Shanjian Tang
Applied Mathematics & Optimization, 2023, 87
[28] Stochastic Galerkin techniques for random ordinary differential equations
Augustin, F.
Rentrop, P.
NUMERISCHE MATHEMATIK, 2012, 122 (03) : 399 - 419
[29] Stochastic Galerkin techniques for random ordinary differential equations
F. Augustin
P. Rentrop
Numerische Mathematik, 2012, 122 : 399 - 419
[30] A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Stochastic Elliptic PDE with Constrained Control
Tongjun Sun
Wanfang Shen
Benxue Gong
Wenbin Liu
Journal of Scientific Computing, 2016, 67 : 405 - 431

← 1 2 3 4 5 →