The application of simulated annealing to the global optimization of a function on a compact subset of R^d is discussed. For the Langevin algorithm the class of convergent schedules depends on some a priori knowledge about the form of the function. It is shown that this problem disappears by using the simplest annealing algorithm of jump type, which can also be improved by performing local searches between two consecutive jump times. The resulting algorithm is essentially a multistart technique controlled by an annealing schedule.