  This paper considers the problem of computing the schedule of modes in a
switched dynamical system, that minimizes a cost functional defined on the
trajectory of the system's continuous state variable. A recent approach to such
optimal control problems consists of algorithms that alternate between
computing the optimal switching times between modes in a given sequence, and
updating the mode-sequence by inserting to it a finite number of new modes.
  These algorithms have an inherent inefficiency due to their sparse update of
the mode-sequences, while spending most of the computing times on optimizing
with respect to the switching times for a given mode-sequence. This paper
proposes an algorithm that operates directly in the schedule space without
resorting to the timing optimization problem. It is based on the Armijo step
size along certain Gateaux derivatives of the performance functional, thereby
avoiding some of the computational difficulties associated with discrete
scheduling parameters. Its convergence to local minima as well as its rate of
convergence are proved, and a simulation example on a nonlinear system exhibits
quite a fast convergence.
