In this paper optimal control problems for switched autonomous systems are studied. In particular, we focus on problems in which a prespecified sequence of active subsystems is given, and propose an approach for finding the optimal switching instants. The approach derives the derivatives of the cost with respect to the switching instants, and uses nonlinear optimization techniques to locate the optimal switching instants. The approach is then applied to general quadratic problems for switched linear autonomous systems and to reachability problems. Examples illustrate the results.