On convergence rate of a rectangular partition based global optimization algorithm

James Calvin; Gražina Gimbutienė; William O. Phillips; Antanas Žilinskas

doi:10.1007/s10898-018-0636-z

On convergence rate of a rectangular partition based global optimization algorithm

James Calvin, Gražina Gimbutienė, William O. Phillips, Antanas Žilinskas

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

14 Scopus citations

Abstract

The convergence rate of a rectangular partition based algorithm is considered. A hyper-rectangle for the subdivision is selected at each step according to a criterion rooted in the statistical models based theory of global optimization; only the objective function values are used to compute the criterion of selection. The convergence rate is analyzed assuming that the objective functions are twice- continuously differentiable and defined on the unit cube in d-dimensional Euclidean space. An asymptotic bound on the convergence rate is established. The results of numerical experiments are included.

Original language	English (US)
Pages (from-to)	165-191
Number of pages	27
Journal	Journal of Global Optimization
Volume	71
Issue number	1
DOIs	https://doi.org/10.1007/s10898-018-0636-z
State	Published - May 1 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics
Business, Management and Accounting (miscellaneous)
Computer Science Applications
Management Science and Operations Research

Keywords

Bayesian approach
Convergence rate
Global optimization
P-algorithm
Rectangular partition
Statistical models for global optimization

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10.1007/s10898-018-0636-z

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AU - Gimbutienė, Gražina

AU - Phillips, William O.

AU - Žilinskas, Antanas

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Y1 - 2018/5/1

N2 - The convergence rate of a rectangular partition based algorithm is considered. A hyper-rectangle for the subdivision is selected at each step according to a criterion rooted in the statistical models based theory of global optimization; only the objective function values are used to compute the criterion of selection. The convergence rate is analyzed assuming that the objective functions are twice- continuously differentiable and defined on the unit cube in d-dimensional Euclidean space. An asymptotic bound on the convergence rate is established. The results of numerical experiments are included.

AB - The convergence rate of a rectangular partition based algorithm is considered. A hyper-rectangle for the subdivision is selected at each step according to a criterion rooted in the statistical models based theory of global optimization; only the objective function values are used to compute the criterion of selection. The convergence rate is analyzed assuming that the objective functions are twice- continuously differentiable and defined on the unit cube in d-dimensional Euclidean space. An asymptotic bound on the convergence rate is established. The results of numerical experiments are included.

KW - Bayesian approach

KW - Convergence rate

KW - Global optimization

KW - P-algorithm

KW - Rectangular partition

KW - Statistical models for global optimization

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ER -

On convergence rate of a rectangular partition based global optimization algorithm

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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