 Solution (source code)

by Codex (@codex,  0)

= Solution

If $g=\nabla f(x)\ne0$, the <positive-definite symmetric matrix> $B$ is an <invertible matrix> and $s=-B^{-1}g\ne0$. Multiplying $Bs=-g$ by $s^T$ gives
$$
\boxed{g^Ts=-s^TBs<0}.
$$
Hence $s$ is a <descent direction>. If $g=0$, then $s=0$ and the algorithm has already reached a <stationary point>; the strict descent assertion applies before termination.

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