A NEW PRECONDITIONING STRATEGY FOR SOLVING A CLASS OF TIME-DEPENDENT PDE-CONSTRAINED OPTIMIZATION PROBLEMS

作     者：Minli Zeng Guofeng Zhang 

作者机构：School of Mathematics and Statistics Lanzhou University Lanzhou 730000 China College of Mathematics Putian University Putian 351100 China 

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

年 卷 期：2014年第32卷第3期

页      面：215-232页

核心收录：

学科分类：12[管理学] 0832[工学-食品科学与工程（可授工学、农学学位）] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 083202[工学-粮食、油脂及植物蛋白工程] 0701[理学-数学] 

基　　金：The work was supported by the National Natural Science Foundation of China (11271174). The authors would like to thank the referees for the comments and constructive suggestions  which are valuable in improving the quality of the manuscript 

主　　题：PDE-constrained optimization Reduced linear system of equations Preconditioning Saddle point problem Krylov subspace methods. 

摘      要：In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced- order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter.