where the notation <·, ·> denotes the l2-inner product. Suppose <·, l> is a linearized functional of interest on P. Given a parameter perturbation δp, the forward functional sensitivity is then given by <F'(p)δp, l>. The same sensitivity can be obtained via the adjoint solution, ψ ≡ F'*(p)l. From the definition of the adjoint operator (3), it follows that: