In this paper, we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion. This stopping criterion is defined by a smooth surface in the state space; when the state trajectory hits this surface, the governing dynamic system stops. By restricting the controls to piecewise constant functions, we derive a finite-dimensional approximation of the optimal control problem. We then develop an efficient computational method, based on nonlinear programming, for solving the approximate problem. We conclude the paper with four numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.