中文摘要：

通过分析Bai （Bai Z Z.Block preconditioners for elliptic PDE-constrained optimization problems.Computing,2011,91：379-395）给出的离散分布控制问题的块反对角预处理线性系统,提出了该问题的一个等价线性系统,并且运用带有预处理子的最小残量方法对该系统进行求解.理论分析和数值实验结果表明,所提出的预处理最小残量方法对于求解该类椭圆型偏微分方程约束最优分布控制问题非常有效,尤其当正则参数适当小的时候.

英文摘要：

By analyzing the block-counter-diagonal preconditioned linear system resulting from discretizations of the distributed control problems proposed in Bai＇s results （Bai Z Z. Block preconditioners for elliptic PDE-constrained optimization problems. Computing, 2011, 91： 379-395）, we derive a new equivalent linear system and apply the MINRES method coupled with a block-diagonal preconditioner to solving it. Theoretical analyses and experiments show that the proposed preconditioned MINRES method is efficient for solving the elliptic PDE-constrained optimization distributed control problems, especially when the regularization parameter is suitably small.