I have a problem to find the optimum diagonal matrix $D$, which would maximizes the number of elements in $ADB$ which are above a certain positive number $\gamma$.
In other words, the problem is stated as follows,
\begin{align} & \max_D \mathrm{sum}(ADB \geq \gamma) \\ & D \in R_+^{n \times n} \text{ is a positive diagonal matrix} \\ & A \in R^{n \times n} \text{ is a symmetric Z-matrix} \\ & B \in R_+^{n \times n} \text{ is a symmetric positive matrix} \end{align}
Z-matrix is a matrix with all non-diagonal entries being nonpositive.
Can anyone help me please?