Let $A\in\mathbb{C}^{m\times n}$, $B\in\mathbb{C}^{n\times k}$, $C\in\mathbb{C}^{k\times m}$ be given complex matrices. The objective of the optimization problem is
\begin{equation}
\mathop {\arg \min }\limits_X \lambda_{\max} \left( (A + BXC)(A + BXC)^H \right),
\end{equation}
where $X\in\mathbb{C}^{k\times k}$ is a matrix with $||x(i,j)||<1$?