In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of the saddle point problem and approximations of the corresponding Schur complement. The spectral properties of the preconditioned matrix is analyzed. Numerical experiments are conducted to demonstrate the effectiveness of the proposed preconditioning method.

翻译：本文针对混合边界条件下椭圆边界最优控制问题产生的鞍点问题，研究其预处理方法。基于鞍点问题的置换及相应Schur补的近似，提出了一种块三角预处理方法。文中分析了预处理矩阵的谱特性，并通过数值实验验证了所提预处理方法的有效性。