Formulation of a SDP problem in a standard form with constraints on blocks

Question

I have a semidefinite problem, \begin{align} \min_{\beta,\eta,R} &t\notag\\ \textrm{s.t.} & \beta ,\eta \geq 0\notag\\ &\Bigl[\begin{matrix} K\odot R&&1+\eta-\beta\\ (1+\eta-\beta)^\mathsf{T}&(t-\eta^\mathsf{T} a -\beta^\mathsf{T} b) \end{matrix}\Bigr] \succcurlyeq 0\notag\\ & R \succcurlyeq 0\notag\\ &\langle R,e_i e_j^\mathsf{T} \rangle = h_{ij},\forall i,j \epsilon H\notag\\ \end{align} where $\odot$ is the matrix hadamard (element-wise) product, and $\langle R,e_i e_j^\mathsf{T} \rangle =trace(R^\mathsf{T} e_i e_j^\mathsf{t}) $. I want to code this problem using any of standard solvers, esp,MOSEK. But these solvers accept the problem in a standard format. How to convert this problem to a standard SDP formulations such as the standard form for mosk? (I need to code it directly in a standard solver, and not using YALIMP or CVX.)