 which, in turn, implies that $p_\mu({\bf f},{\boldsymbol \lambda})$ is $\epsilon$-convex. In particular, if there exists $i_0\in I$ such that $f_{i_0}$ is $\epsilon_{i_0}$-strongly convex, then $p_\mu({\bf f},{\boldsymbol \lambda})$ is $\epsilon$-strongly convex.  