Average performance of a class of adaptive algorithms for global optimization

We describe a class of adaptive algorithms for approximating the global minimum of a continuous function on the unit interval. The limiting distribution of the error is derived under the assumption of Wiener measure on the objective functions. For any δ > 0, we construct an algorithm which has error converging to zero at rate n(-1-δ). in the number of function evaluations n. This convergence rate contrasts with the n-1/2 rate of previously studied nonadaptive methods.