A lower bound on complexity of optimization on the Wiener space

James M. Calvin

doi:10.1016/j.tcs.2007.04.016

A lower bound on complexity of optimization on the Wiener space

James M. Calvin

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

5 Scopus citations

Abstract

This paper is a study of the complexity of optimization of continuous univariate functions using a fixed number of sequentially selected function evaluations. The complexity is studied in the average case under a conditioned Wiener measure. We show that to obtain an error of at most ε{lunate}, on the order of log log (1 / ε{lunate}) log (1 / ε{lunate}) function evaluations are required.

Original language	English (US)
Pages (from-to)	132-139
Number of pages	8
Journal	Theoretical Computer Science
Volume	383
Issue number	2-3
DOIs	https://doi.org/10.1016/j.tcs.2007.04.016
State	Published - Sep 18 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Keywords

Average-case complexity
Global optimization
Wiener measure

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10.1016/j.tcs.2007.04.016

Cite this

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AB - This paper is a study of the complexity of optimization of continuous univariate functions using a fixed number of sequentially selected function evaluations. The complexity is studied in the average case under a conditioned Wiener measure. We show that to obtain an error of at most ε{lunate}, on the order of log log (1 / ε{lunate}) log (1 / ε{lunate}) function evaluations are required.

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A lower bound on complexity of optimization on the Wiener space

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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