If B were affine, which it is not, the objective function -lambda_min(B)would be convex, and therefore maximizing it would be non-convex. So you either need to formulate a provably convex optimization problem, or use a different tool for this problem.
If you wish to pursue this further, please open a new thread. It becomes confusing when more than one problem is addressed in a given thread, unless perhaps they are closely related.