Maximize $\text{trace}(Z^{T}A Z)/\text{trace}(Z^{T}B Z)$

Question

I am trying to find $Z$ in the following problem:

\begin{equation} \begin{array}{c} maximize \hspace{2mm} \frac{\text{trace}(Z^{T}Lb\hspace{2mm} Z)}{\text{trace}(Z^{T}Lw\hspace{2mm} Z)}, \\ \end{array} \end{equation} for $Z \in \mathbb{R}^{m\times n}$ and $Wb,Ww \in \mathbb{R}^{mxm}$. Using the scale constraint \begin{equation} Z^{T} Dw Z = I \end{equation} And Lw = Dw −Ww , Lb = Db −Wb.(Laplacian)

W(Wb,Ww) denotes the symmetric affinity matrix and D(Db,Dw) is the diagonal weight matrix, whose entries are column (or row, since W is symmetric) sums of W, then the Laplacian matrix is given L = D −W.

I would appreciate any help!

What are A,B,Z? What do you mean by $Z^\prime$? Over what set are you considering the maximum? You should clarify your question by explaining your notation. — Angelo Lucia, Jan 06 '15 at 10:53
A B and Z are matrixes.. Z':transpose(Z)..I am trying to find Z.. Thank you — user205035, Jan 06 '15 at 10:57
Are they real or complex? What size do they have? What constrains do you have on the maximum? Your question still does not make sense to me. — Angelo Lucia, Jan 06 '15 at 10:58
W(Wb,Ww) denotes the symmetric affinity matrix and D(Db,Dw) is the diagonal weight matrix, whose entries are column (or row, since W is symmetric) sums of W, then the Laplacian matrix is given L = D −W. — user205035, Jan 06 '15 at 12:05