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August 1997 Average performance of a class of adaptive algorithms for global optimization
James M. Calvin
Ann. Appl. Probab. 7(3): 711-730 (August 1997). DOI: 10.1214/aoap/1034801250

Abstract

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.

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James M. Calvin. "Average performance of a class of adaptive algorithms for global optimization." Ann. Appl. Probab. 7 (3) 711 - 730, August 1997. https://doi.org/10.1214/aoap/1034801250

Information

Published: August 1997
First available in Project Euclid: 16 October 2002

zbMATH: 1008.90518
MathSciNet: MR1459267
Digital Object Identifier: 10.1214/aoap/1034801250

Subjects:
Primary: 60J65 , 68Q25
Secondary: 11Y16 , 73K40

Keywords: average complexity , Brownian motion , global optimization

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 3 • August 1997
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