I recently encountered the following optimization problem:
$\max \|AX\|_F^2$
subject to: $X\succeq0$ and $Xb_i\leq c_i$ for a collection of $T$ conditions: $i=1,\ldots,T$.
Matrices $A$ and $X$ are square and symmetric, and $c$ is a column vector.
I know from Wikipedia that the general "quadratically constrained quadratic optimization" problem is NP-hard. However, can this special form be solved efficiently?
Thanks a lot!