Would you please help in solving the following:
$\mathop {\min }\limits_{\mathbf{G}_{\textrm{p}}}\hspace{5pt} \hspace{4pt} \textrm{trace} \Big(\mathbf {G}_{\textrm{tx}}\mathbf {G}_{\textrm{p}} \mathbf{D}_{\textrm{o}}\mathbf {G}_{\textrm{p}}^{{\textrm{H}}}\mathbf {G}_{\textrm{tx}}^{{\textrm{H}}}\Big)$
$\textrm{s.t.}: \hspace{5pt} {\textrm{trace}\left(\mathbf {G}_{\textrm{p}} \mathbf{D}_{j}\mathbf {G}_{\textrm{p}}^{{\textrm{H}}}\mathbf{J}\right)}\nonumber \geq \gamma_{k} \bigg[\textrm{trace}\Big( \mathbf{Q}_{\textrm{n}k}\Big) +\textrm{trace}\left( \mathbf {G}_{\textrm{p}} \mathbf{D}_{\textrm{n}}\mathbf{G}_{\textrm{p}}^{{\textrm{H}}}\mathbf{J}\right)\bigg] \\$
$ \hspace{22pt} {\mathbf{G}_{\textrm{p}}} \textrm{ Diagonal}\label{cons1}$
$\hspace{22pt} {\mathbf{G}_{\textrm{p}}} \succeq 0$
$\hspace{22pt} \textrm{Tr} \left ( {\mathbf{G}_{\textrm{p}}}{\mathbf{G}_{\textrm{p}}}^{{\textrm{H}}} \right )\leq P_{\textrm{r}},$
All matrices are positive semidefinite. How can we find the solution?