 Wolfe conditions

For a continuously differentiable function, a descent direction $s$ and $0<{\beta }_1<{\beta }_2<1$, the Wolfe conditions require both the Armijo condition andThis second inequality is the weak curvature condition: the slope must have become less negative. The strong variant instead requires $|\nabla f(x+\alpha s{)}^{T}s|\le {\beta }_2|\nabla f(x{)}^{T}s|$. The weak version already guarantees a positive curvature pair for the Quasi-Newton secant equation.