Here is my problem to be solve:

\underset{\gamma, z, X}{\text{inf}}\,\, \gamma c +z\\
\,\,\,\,\,\text{s.t.} \,\, \gamma\geq 0\\
\,\,\,\,\,\begin{bmatrix} \gamma I-X & \gamma v \\ (\gamma v)^T & z \\ \end{bmatrix} \succeq 0\\
\,\,\,\,\,X_{ij} = 1 ,\,\, \text{for}\,\, i ==j\\
\,\,\,\,\,X_{ij} <0 ,\,\, \text{for}\,\, i \neq j

c,v are constant value and vector. \gamma, z, X are decision variables and decision matrix. X is a symetric matrix. When I try to use cvx to solve this question, I encounter the following problem. The objective function and first two constraints are simple to handle in cvx. However, how can I handle the last two constraints in cvx？That is , in cvx, how should I handle the matrix diagnal and off-diagnal constraints (X_{ij} = 1 ,\,\, \text{for}\,\, i ==j,X_{ij} <0 ,\,\, \text{for}\,\, i \neq j)?