Geometry and combinatorics of the cutting angle method

Beliakov, Gleb 2003, Geometry and combinatorics of the cutting angle method, Optimization, vol. 52, no. 4-5, pp. 379-394.

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Title Geometry and combinatorics of the cutting angle method
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb
Journal name Optimization
Volume number 52
Issue number 4-5
Start page 379
End page 394
Publisher Taylor & Francis
Place of publication London, England
Publication date 2003-08
ISSN 0233-1934
Keyword(s) 90C59
cutting angle method
global optimization
lipschitz optimization
random number generator
saw tooth cover
Summary Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.
Language eng
Field of Research 020599 Optical Physics not elsewhere classified
Socio Economic Objective 970102 Expanding Knowledge in the Physical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2003, Taylor & Francis
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