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.
Publié le : 1997-08-14
Classification:
Brownian motion,
global optimization,
average complexity,
60J65,
68Q25,
11Y16,
73K40
@article{1034801250,
author = {Calvin, James M.},
title = {Average performance of a class of adaptive algorithms for global
optimization},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 711-730},
language = {en},
url = {http://dml.mathdoc.fr/item/1034801250}
}
Calvin, James M. Average performance of a class of adaptive algorithms for global
optimization. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 711-730. http://gdmltest.u-ga.fr/item/1034801250/