Average performance of a class of adaptive algorithms for global optimization

Abstract

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 $\delta > 0$, we construct an algorithm which has error converging to zero at rate $n^{(-1-\delta)}$. in the number of function evaluations n. This convergence rate contrasts with the $n^{-1/2}$ rate of previously studied nonadaptive methods.