Some transformation techniques with applications in global optimization

Authors:
Andreas Lundell;Joakim Westerlund;Tapio Westerlund
Affiliations:
Process Design Laboratory, Åbo Akademi University, Turku, Finland 20500;Process Design Laboratory, Åbo Akademi University, Turku, Finland 20500;Process Design Laboratory, Åbo Akademi University, Turku, Finland 20500
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

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.