For example consider the problem
$\min_X f(X)$
s.t. $\lambda_i(X+A)=\lambda_i(B)$ for $i \in {1,...,N}$
where $A$ and $B$ are full rank N by N matrix, $\lambda_i(X)$ is the i-th eigenvalue of $X$
Is it the correct way to represent the eigenvalue constraints?
If yes, how can it be handled?