^*$ is Fréchet differentiable on ${\ensuremath{\mathcal H}}$ and that ${\ensuremath{\mathcal{R}_{\mu}({\bf A},{\boldsymbol \lambda})}}=\partial p_\mu({\bf f},{\boldsymbol \lambda})=\nabla p_\mu({\bf f},{\boldsymbol \lambda})$ is $\epsilon$-Lipschitz where