I'm having problem with formulating dual problem to Semidefinite programing problem: $$\max\;\;tr(X)$$
$$s.t.\;\; \left[ \begin{array}{cc} A & X \\ X & B \end{array} \right]\succeq0$$
where A, B are symmetric and positive definite matricies and X is symmetric.
It is known that a general SDP has the following Primar Dual pair:
$$P) \;\; \min \;\; tr(C^TX)$$
$$s.t.\;\; tr(A_{i}^TX)=b_i\;\;i=1,...,m$$ $$X\succeq 0$$
$$D)\;\; \max b^Ty$$
$$s.t.\;\; \sum_{i=1}^{m}A_iy_i + S = C $$ $$S\succeq0$$
however, I cannot find a way, how to reformulate it. Thank You