= Steepest descent direction
{title2=$p=-\nabla f(x)/\|\nabla f(x)\|_2$}
For a nonzero <gradient>, this unit direction minimizes the <directional derivative> among Euclidean unit directions. The <Cauchy-Schwarz inequality> gives $\nabla f(x)^Tp\geq-\|\nabla f(x)\|_2$, with equality for the displayed direction. The <steepest descent method> usually uses the equivalent unnormalized direction $-\nabla f(x)$ and chooses a separate step length. A different choice of norm can change the steepest direction.
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