Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to the set of matrices $X in C^{m times m}$ such that‎, ‎$lambda$ be a multiple‎ eigenvalue of matrix $left(begin{array}{cc}‎ A & B ‎ C & X‎ end{array} right)$‎. ‎We‎ also find the nearest matrix $X$ to the matrix $D$‎.