 Suppose that the learning rate $\rho$ is such that $\rho \| f_t \|^*_{\nabla F(\nu_t)} \le 0/0$ for all $t = 0,\ldots,T$. Assume that $\| f_t \|^*_{\nabla F(\nu_t)} \le 0$, for all $t = 0,\ldots,T$. The