We study adaptive and nonadaptive methods for Lq-approximation and global optimization based on n function evaluations from a Wiener space sample. We derive (asymptotically) optimal methods with respect to an average error. The error of optimal methods converges to zero with the following rates: n-1 2 for Lq-approximation if 1 ≤ q < ∞, (ln n n)1 2 if q = ∞, and n-1 2 for nonadaptive methods for global optimization. We show that adaption helps for global optimization. © 1990.
Ritter, K. (1990). Approximation and optimization on the Wiener space. Journal of Complexity, 6(4), 337–364. https://doi.org/10.1016/0885-064X(90)90027-B