A lower bound on complexity of optimization under the rr-fold integrated Wiener measure

We consider the problem of approximating the global minimum of an rr-times continuously differentiable function on the unit interval, based on sequentially chosen function and derivative evaluations. Using a probability model based on the rr-fold integrated Wiener measure, we establish a lower bound on the expected number of function evaluations required to approximate the minimum to within ϵϵ on average.