A One-Dimensional Optimization Algorithm and Its Convergence Rate under the Wiener Measure

Document Type

Article

Publication Date

1-1-2001

Abstract

In this paper we describe an adaptive algorithm for approximating the global minimum of a continuous function on the unit interval, motivated by viewing the function as a sample path of a Wiener process. It operates by choosing the next observation point to maximize the probability that the objective function has a value at that point lower than an adaptively chosen threshold. The error converges to zero for any continuous function. Under the Wiener measure, the error converges to zero at rate e-nδn, where {δn} (a parameter of the algorithm) is a positive sequence converging to zero at an arbitrarily slow rate. © 2001 Academic Press.

Identifier

0035373827 (Scopus)

Publication Title

Journal of Complexity

External Full Text Location

https://doi.org/10.1006/jcom.2001.0574

ISSN

0885064X

First Page

306

Last Page

344

Issue

2

Volume

17

Grant

DMI-9696243

Fund Ref

National Science Foundation

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