 Cauchy decrease bound

Use the induced spectral norm for the symmetric matrix $H$ and interpret $\Vert g\Vert /\Vert H\Vert =+\infty$ when $H=0$. If $q=g^{T}Hg\le 0$, the Cauchy point gives a decrease at least $\Delta \Vert g\Vert$. If $q>0$, its step size satisfies $\tau q\le \Vert g{\Vert }^2$ and $q\le \Vert H\Vert \Vert g{\Vert }^2$, soThus the numerical constant $1/2$ is independent of the model data. The bound links a nonzero gradient to a definite predicted decrease, including for an indefinite matrix $H$.