Approximation and optimization on the Wiener space

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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.

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