Consider the following mixed semi definite and second order programming:

$\begin{array}{l} \mathop {{\rm{min}}}\limits_{\bf{X}} \,{\rm{Tr}}\left( {{\bf{XA}}} \right)\\ {\rm{s}}{\rm{.t:}}\, & {\rm{Tr}}\left( {{\bf{XA'}}} \right) + \left\| {{\rm{vec}}{{\left( {\bf{X}} \right)}^H}{\bf{A''}}} \right\| \ge a\\ & {\bf{X}} \ge {\bf{0}} \end{array}$

where ${\bf{A}}$,${{\bf{A'}}}$ and ${{\bf{A''}}}$ are $M \times M$ positive semi definite matrices, $a$ is a positive constant. $vec(.)$ is the stack column operator. By assumption of feasibility of the above problem, how can I obtain the order of complexity of the mixed semi definite and second order optimization problem?