Search direction
= Search direction
{title2=$x_{j+1}=x_j+\alpha_jp_j$}
A search direction is the nonzero <vector> $p_j$ used in the displayed optimization update. In a <line search> with positive <step size>, its orientation matters: a <descent direction> has negative <directional derivative> of the <objective function>. Minimization over a full line instead permits either sign of $\alpha_j$.