The success of automatic velocity inversion is highly dependent on the numerical tractability of the optimization problem which defines the solution. The purpose of this paper is to compare the objective (cost) functions arising from two different formulations of the problem. It is shown by example that the output least-squares approach defines an objective function which can be highly nonconvex and which can have local, nonglobal minima. In contrast, the method of Differential Semblance Optimization defines a cost function which has a unique minimizer and which appears to be nearly convex. These two approaches are applied to the simple problem of determining the depth of a horizontal reflector and the velocity of the layer above it.