Global optimization via dense curves

Purpose To study constrained or unconstrained global optimization problems in a cube of Rd where d is a positive integer. Designmethodologyapproach dense curves are initially used to transform this problem into a global optimization problem of a single variable. The optimization of the one variable...

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Bibliographic Details
Published in:Kybernetes 2005-08, Vol.34 (7/8), p.999-1011
Main Authors: Benabidallah, A., Cherruault, Y.
Format: Article
Language:English
Subjects:
Algorithms
Cybernetics
Mathematical models
Optimization techniques
Transforms
Online Access:Get full text
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Summary:Purpose To study constrained or unconstrained global optimization problems in a cube of Rd where d is a positive integer. Designmethodologyapproach dense curves are initially used to transform this problem into a global optimization problem of a single variable. The optimization of the one variable is then treated by means of the LegendreFenchel Transform. This discrete convex envelope of the one variable function obtained previously, can then be computed. Findings Global optimization problems of this nature have already been extensively studied by the authors. In this paper they have coupled the Alienor method with LegendreFenchel Tranform to compute a discrete convex envelope of the function to minimize. A fast algorithm was successfully used to do this. Research limitationsimplications This approach to global optimization is based on dense curves and numerical tests performed on a Pentium IV 1,700MHz computer used with Mathematica 4 software. Practical implications Gives the solutions illustrated in the numerous examples provided that show the practicality of the methodology. Originalityvalue A new approach based on extensive research into global optimization via dense curves.
ISSN:0368-492X
1758-7883
DOI:10.1108/03684920510605821