Sample-path optimization is a method for optimizing limit functions occurring in stochastic modeling problems, such as steady-state functions in discrete-event dynamic systems. It is closely related to retrospective optimization techniques and to M-estimation. The method has been computationally tested elsewhere on problems arising in production and in project planning, with apparent success. In this paper we provide a mathematical justification for sample-path optimization by showing that under certain assumptions—which hold for the problems just mentioned—the method will almost surely find a point that is, in a specified sense, sufficiently close to the set of optimizers of the limit function.