Some transformation techniques with applications in global optimization

In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Signomial terms can always be convexified and underestimated using power transformations on th...

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Bibliographic Details
Published in:Journal of global optimization Vol. 43; no. 2-3; pp. 391 - 405
Main Authors: Lundell, Andreas, Westerlund, Joakim, Westerlund, Tapio
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2009
Springer Nature B.V
Subjects:
Approximation
Computer Science
Inequality
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Variables
Mixed integer non-linear programming
Global optimization
Signomial functions
Transformation and convexification techniques
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Signomial terms can always be convexified and underestimated using power transformations on the individual variables in the terms. However, often not all variables need to be transformed. A method for minimizing the number of original variables involved in the transformations is, therefore, presented. In order to illustrate how the given method can be integrated into the transformation framework, some mixed integer optimization problems including signomial functions are finally solved to global optimality using the given techniques.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-007-9223-4