There is one complication here: Any local apparent horizon finding algorithm may fail if the initial guess is not good enough, even if the desired surface is actually present. The solution is to use the constant-expansion surface for a slightly larger expansion E as an initial guess, gradually “walking down” the value of E to find the minimum value E∗. Thornburg [156Jump To The Next Citation Point, Appendix C] describes such a “continuation-algorithm binary search” algorithm in detail.