  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.
