Elsevier

Journal of Complexity

Volume 6, Issue 4, December 1990, Pages 337-364
Journal of Complexity

Regular article
Approximation and optimization on the Wiener space

https://doi.org/10.1016/0885-064X(90)90027-BGet rights and content
Under an Elsevier user license
open archive

Abstract

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−12 for Lq-approximation if 1 ⩽ q < ∞, (ln nn)12 if q = ∞, and n−12 for nonadaptive methods for global optimization. We show that adaption helps for global optimization.

Cited by (0)