An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions

James M. Calvin; Yvonne Chen; Antanas Žilinskas

doi:10.1007/s10957-012-0060-3

An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions

James M. Calvin
, Yvonne Chen
, Antanas Žilinskas

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

17 Scopus citations

Abstract

We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a twice continuously differentiable function.

Original language	English (US)
Pages (from-to)	628-636
Number of pages	9
Journal	Journal of Optimization Theory and Applications
Volume	155
Issue number	2
DOIs	https://doi.org/10.1007/s10957-012-0060-3
State	Published - Nov 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Keywords

Convergence
Optimization
Statistical models

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10.1007/s10957-012-0060-3

Cite this

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title = "An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions",

abstract = "We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a twice continuously differentiable function.",

keywords = "Convergence, Optimization, Statistical models",

author = "Calvin, \{James M.\} and Yvonne Chen and Antanas {\v Z}ilinskas",

note = "Funding Information: Acknowledgements The work of J.M. Calvin and Y. Chen was supported by the National Science Foundation under Grant No. CMMI-0825381, and the work of A. {\v Z}ilinskas was supported by the Research Council of Lithuania under Grant No. MIP-063/2012.",

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AU - Chen, Yvonne

AU - Žilinskas, Antanas

N1 - Funding Information: Acknowledgements The work of J.M. Calvin and Y. Chen was supported by the National Science Foundation under Grant No. CMMI-0825381, and the work of A. Žilinskas was supported by the Research Council of Lithuania under Grant No. MIP-063/2012.

PY - 2012/11

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N2 - We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a twice continuously differentiable function.

AB - We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a twice continuously differentiable function.

KW - Convergence

KW - Optimization

KW - Statistical models

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UR - https://www.scopus.com/pages/publications/84869110921#tab=citedBy

U2 - 10.1007/s10957-012-0060-3

DO - 10.1007/s10957-012-0060-3

M3 - Article

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SN - 0022-3239

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IS - 2

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An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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