The plane-wave detection problem is: to estimate the incidence angle and waveform of a transient plane traveling wave, from samples recorded at a linear array of receivers. This simple problem shares several important mathematical features with other inverse problems of wave propagation, and is of interest in its own right as a model problem in ocean acoustic signal analysis. Straightforward formulation as a nonlinear least squares problem yields a nonconvex objective for which the minima are not stably dependent on the data. In contrast, an infeasible point formulation, in which the signal at each receiver is explained to some extent independently, proves to yield a smooth convex optimization problem with stable optima. Numerical experiments illustrate the theoretical results about the infeasible point approach, differential semblance optimization.