I am trying to solve the following problem:
$\max_{X} \operatorname{trace} \left( AX^TBX\right).$
A and B is given.
$A$ is a $n\times n$ symmetric matrix and $B$ is a $n\times n$ nonnegative positive definite symmetric matrix.
$X$ is a $n\times n$ diagonal matrix.
Are there any experts aware of this optimization problem?We kindly ask for your cooperation.