Before revision:  The marginal optimization map is nonlinear and not differentiable, which complicates inference procedures, since statistical inference methods for nonlinear maps usually rely on regularity through a type of differentiability.
After revision:  Marginal optimization is not compactly differentiable as a map between the spaces of objective and value functions, which is problematic because standard inference methods for nonlinear maps usually rely on regularity through a type of differentiability.