c must equal b’.
If using SDP mode (cvx_begin sdp) of CVX, include the constraint
[a b;b' d] >= 0 to specify that
[a b;b' d] is positive semidefinite.
ff not using SDP mode (cvx_begin) of CVX, include the constraint
[a b;b' d] == semidefinite(n) , where n is the dimension of
[a b;b' d].
The above doesn’t address Schur complement representation per se. The Schur complement representation involves figuring out which matrix you want to constrain to be positive semidefinite. For instance, see section A.5.5 of http://stanford.edu/~boyd/cvxbook/ . You can search for
Schur complement in that book for examples of how to use Schur complements in problem (re)formulation.