Average performance of a class of adaptive algorithms for global optimization

James M. Calvin

doi:10.1214/aoap/1034801250

Average performance of a class of adaptive algorithms for global optimization

James M. Calvin

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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 δ > 0, we construct an algorithm which has error converging to zero at rate n^{-(1 - δ)} in the number of function evaluations n. This convergence rate contrasts with the n^11/2 rate of previously studied nonadaptive methods.

Original language	English (US)
Pages (from-to)	711-730
Number of pages	20
Journal	Annals of Applied Probability
Volume	7
Issue number	3
DOIs	https://doi.org/10.1214/aoap/1034801250
State	Published - Aug 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Average complexity
Brownian motion
Global optimization

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10.1214/aoap/1034801250

Cite this

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AB - 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 δ > 0, we construct an algorithm which has error converging to zero at rate n-(1 - δ) in the number of function evaluations n. This convergence rate contrasts with the n11/2 rate of previously studied nonadaptive methods.

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KW - Brownian motion

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Average performance of a class of adaptive algorithms for global optimization

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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