Is it possible to give a closed form solution to the value or minimizer to the following problem? $$ \inf \{ \|AX + B\|_{\rm op} : \|X\|_{F} = 1\} $$ Above, $A, X, B$ are square matrices, and $\|\cdot\|_{\rm op}$ is the operator norm, also given by the largest singular value, for instance. $\|\cdot\|_F$ is Frobenius norm (sometimes also called Hilbert-Schmidt norm). We can assume that $A, B$ are invertible.
An easy case is when the dimension is 1: $$ \inf\{|ax + b| : |x| = 1\} = \min\{|a - b|, |a + b|\}. $$ Is there a way to generalize this for larger dimensions?