There is a simple heuristic argument (see, for example, Press et al. [125Jump To The Next Citation Point, Section 9.6]) that at least some spurious local minima should be expected. We are trying to solve a system of Nang nonlinear equations, Θi = 0 (one equation for each horizon-surface grid point). Equivalently, we are trying to find the intersection of the Nang codimension-one hypersurfaces Θi = 0 in surface-shape space. The problem is that anywhere two or more of these hypersurfaces approach close to each other, but do not actually intersect, there is a spurious local minimum in ∥Θ∥.