Line search
= Line search
A <line search> chooses a positive <step size> $\alpha$ along a search <vector> $s$, updating $x$ to $x+\alpha s$. For a <differentiable function> $f$, a <descent direction> makes sufficiently short steps decrease the <objective function>; an <Armijo condition> quantifies the decrease, while the <Wolfe conditions> also prevent accepting an unnecessarily short step.