The main focus of much of the analysis of optimization algorithms is on global convergence to critical points, and complexity estimates thereof. For convex optimization this is unquestionably where the focus should be. But for nonconvex problems, it is of dubious value to have an algorithm that provably races faster than others to a critical point that is useless from an application standpoint.
We present an analysis of algorithms for nonconvex optimzation that takes into account the quality of fixed points in terms of the optimization model; this leads to a criterion that can be used to recommend some algorithms over others. We show how this analysis works for the case of orbital tomography, or the problem of observing molecular electronic orbitals from sparse data.