Termination Criteria

Given small tolerance, $ϵ>0$. Stop the loop when $x_k$ fulfills.

$$\begin{array}{rlr}& 1.& ||\nabla f(x^{\ast })||<ϵ\\ & 2.& ||x_k-x_{k-1}||\le ϵ\\ & 3.& ||f(x_k)-f(x_{k-1})||\le ϵ\\ & 4.& k>k_{max}\end{array}$$