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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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
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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.
AbstractList	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. Issue Title: Mykonos Go conference 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.
Author	Lundell, Andreas Westerlund, Tapio Westerlund, Joakim
Author_xml	– sequence: 1 givenname: Andreas surname: Lundell fullname: Lundell, Andreas organization: Process Design Laboratory, Åbo Akademi University – sequence: 2 givenname: Joakim surname: Westerlund fullname: Westerlund, Joakim organization: Process Design Laboratory, Åbo Akademi University – sequence: 3 givenname: Tapio surname: Westerlund fullname: Westerlund, Tapio email: tapio.westerlund@abo.fi organization: Process Design Laboratory, Åbo Akademi University
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Cites_doi	10.1023/A:1021091110342 10.1007/BF01580653 10.1016/S0098-1354(96)00282-7 10.1007/BF00933404 10.1016/S0098-1354(02)00254-5 10.1007/BF01097059 10.1016/S1570-7946(00)80002-4
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Keywords	Mixed integer non-linear programming Global optimization Signomial functions Transformation and convexification techniques
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References	Westerlund, Westerlund (CR11) 2003; 3 CR2 Björk, Lindberg, Westerlund (CR3) 2003; 27 CR4 Rijckaert, Martens (CR8) 1978; 26 Maranas, Floudas (CR5) 1995; 7 CR7 Beale, Forrest (CR1) 1976; 10 Maranas, Floudas (CR6) 1997; 21 CR9 Westerlund, Pörn (CR10) 2002; 3 9223_CR9 9223_CR7 T. Westerlund (9223_CR11) 2003; 3 C.D. Maranas (9223_CR6) 1997; 21 K.-M. Björk (9223_CR3) 2003; 27 9223_CR4 T. Westerlund (9223_CR10) 2002; 3 9223_CR2 C.D. Maranas (9223_CR5) 1995; 7 E.M.L. Beale (9223_CR1) 1976; 10 M.J. Rijckaert (9223_CR8) 1978; 26
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Title	Some transformation techniques with applications in global optimization
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