$ is Fréchet differentiable on ${\ensuremath{\mathcal H}}$ and ${\ensuremath{\mathcal{R}_{\mu}({\bf A},{\boldsymbol \lambda})}}=\nabla p_\mu({\bf f},{\boldsymbol \lambda})$ is $\epsilon$-Lipschitz where $\epsilon=r_\mu(\boldsymbol{\epsilon},\boldsymbol{\lambda})$.  Fact \[Zal strong convexity iff\] guarantees that 