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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| Vydané v: | Journal of global optimization Ročník 43; číslo 2-3; s. 391 - 405 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Boston
Springer US
01.03.2009
Springer Nature B.V |
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| 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. |
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| 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 |
| References_xml | – ident: CR9 – volume: 3 start-page: 253 year: 2002 end-page: 280 ident: CR10 article-title: Solving pseudo-convex mixed-integer problems by cutting plane techniques publication-title: Optim. Eng. doi: 10.1023/A:1021091110342 – volume: 10 start-page: 52 year: 1976 end-page: 69 ident: CR1 article-title: Global optimization using special ordered sets publication-title: Math. Program. doi: 10.1007/BF01580653 – volume: 21 start-page: 351 year: 1997 end-page: 370 ident: CR6 article-title: Global optimization in generalized geometric programming publication-title: Comp. Chem. Eng. doi: 10.1016/S0098-1354(96)00282-7 – volume: 26 start-page: 205 issue: 2 year: 1978 end-page: 242 ident: CR8 article-title: Comparison of generalized geometric programming algorithms publication-title: J. Optim.Theory Appl. doi: 10.1007/BF00933404 – volume: 27 start-page: 669 year: 2003 end-page: 679 ident: CR3 article-title: Some convexifications in global optimization of problems containing signomial terms publication-title: Comp. Chem. Eng. doi: 10.1016/S0098-1354(02)00254-5 – ident: CR7 – ident: CR4 – ident: CR2 – volume: 3 start-page: 1045 year: 2003 end-page: 1050 ident: CR11 article-title: GGPECP—an algorithm for solving non-convex MINLP problems by cutting plane and transformation techniques publication-title: Chem. Eng. Trans. – volume: 7 start-page: 143 year: 1995 end-page: 182 ident: CR5 article-title: Finding all solutions of nonlinearly constrained systems of equations publication-title: J. Global Optim. doi: 10.1007/BF01097059 – ident: 9223_CR9 – ident: 9223_CR4 – ident: 9223_CR7 doi: 10.1016/S1570-7946(00)80002-4 – volume: 3 start-page: 1045 year: 2003 ident: 9223_CR11 publication-title: Chem. Eng. Trans. – volume: 7 start-page: 143 year: 1995 ident: 9223_CR5 publication-title: J. Global Optim. doi: 10.1007/BF01097059 – ident: 9223_CR2 – volume: 21 start-page: 351 year: 1997 ident: 9223_CR6 publication-title: Comp. Chem. Eng. doi: 10.1016/S0098-1354(96)00282-7 – volume: 3 start-page: 253 year: 2002 ident: 9223_CR10 publication-title: Optim. Eng. doi: 10.1023/A:1021091110342 – volume: 27 start-page: 669 year: 2003 ident: 9223_CR3 publication-title: Comp. Chem. Eng. doi: 10.1016/S0098-1354(02)00254-5 – volume: 26 start-page: 205 issue: 2 year: 1978 ident: 9223_CR8 publication-title: J. Optim.Theory Appl. doi: 10.1007/BF00933404 – volume: 10 start-page: 52 year: 1976 ident: 9223_CR1 publication-title: Math. Program. doi: 10.1007/BF01580653 |
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