The problem is \begin{eqnarray} \max_\mathbf{x} \,&& \frac{\mathbf{x}^H\mathbf{R}\mathbf{x}}{\mathbf{x}^H\mathbf{x}}, \\ \textrm{s.t.,} && \mathbf{x}(1:s) = \mathbf{d}, \end{eqnarray} where $\mathbf{x}$ is a complex-valued vector of dimension $N$, $\mathbf{R}$ is a positive definite Hermitian matrix. The constraint means that the first $s$ entries of the vector $\mathbf{x}$ is fixed to be $\mathbf{d}$.
I understand that without the constraint, the solution is the dominant eigenvector of $\mathbf{R}$. Then how about with the constraint? Thanks a lot.