On a Global Optimization Algorithm for Bivariate Smooth Functions

James M. Calvin; Antanas Žilinskas

doi:10.1007/s10957-014-0531-9

On a Global Optimization Algorithm for Bivariate Smooth Functions

James M. Calvin, Antanas Žilinskas

Computer Science

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

7 Scopus citations

Abstract

The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided.

Original language	English (US)
Pages (from-to)	528-547
Number of pages	20
Journal	Journal of Optimization Theory and Applications
Volume	163
Issue number	2
DOIs	https://doi.org/10.1007/s10957-014-0531-9
State	Published - Oct 7 2014

All Science Journal Classification (ASJC) codes

Management Science and Operations Research
Control and Optimization
Applied Mathematics

Keywords

Convergence
Decision theory
Delaunay triangulation
Global optimization

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10.1007/s10957-014-0531-9

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title = "On a Global Optimization Algorithm for Bivariate Smooth Functions",

abstract = "The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided.",

keywords = "Convergence, Decision theory, Delaunay triangulation, Global optimization",

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

note = "Funding Information: Acknowledgments The work of J. Calvin 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. The remarks of unknown referees were very helpful to improve the readability of the paper. Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

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AU - Žilinskas, Antanas

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N2 - The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided.

AB - The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided.

KW - Convergence

KW - Decision theory

KW - Delaunay triangulation

KW - Global optimization

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ER -

On a Global Optimization Algorithm for Bivariate Smooth Functions

Abstract

All Science Journal Classification (ASJC) codes

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