= Wolfe conditions
{c}
{wiki}
For a <continuously differentiable function>, a <descent direction> $s$ and $0<\beta_1<\beta_2<1$, the <Wolfe conditions> require both the <Armijo condition> and
$$
\nabla f(x+\alpha s)^Ts\geq\beta_2\nabla f(x)^Ts.
$$
This second inequality is the weak curvature condition: the slope must have become less negative. The strong variant instead requires $|\nabla f(x+\alpha s)^Ts|\leq\beta_2|\nabla f(x)^Ts|$. The weak version already guarantees a positive curvature pair for the <Quasi-Newton secant equation>.
Back to article page
