This image is from Appendix B.1 in Convex Optimization by Stephen Boyd.
My question is: how is B.2. enforcing the constraint $b_{0} + \lambda b_{1} \in R(A_{0} + \lambda A_{1})$ which is described in the dual function. Is B.2. a relaxation of the dual or the exact dual?
I don't have enough reputation to leave a comment, but if you read section A.5 of Boyd's book there is a section titled "Schur Complement with Singular $A$". This part states that for the block matrix to be positive semidefinite, the range condition you mention must be satisfied.