Multi-parametric disaggregation technique for global optimization of polynomial programming problems

This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of...

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Published in:	Journal of global optimization Vol. 55; no. 2; pp. 227 - 251
Main Authors:	Teles, João P., Castro, Pedro M., Matos, Henrique A.
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01.02.2013 Springer Springer Nature B.V
Subjects:	Approximation Computer Science Costs Engineering Heat exchangers Linear programming Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Maximization Operations Research/Decision Theory Optimization Polynomials Production planning Programming Real Functions Studies Transformations Variables Polynomial Signomial Parameterization Optimization Mixed-integer linear programming
ISSN:	0925-5001, 1573-2916
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Abstract	This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach.
AbstractList	This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach. Keywords Polynomial * Signomial * Optimization * Mixed-integer linear programming * Parameterization This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach. This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach.[PUBLICATION ABSTRACT]
Audience	Academic
Author	Castro, Pedro M. Teles, João P. Matos, Henrique A.
Author_xml	– sequence: 1 givenname: João P. surname: Teles fullname: Teles, João P. organization: Laboratório Nacional de Energia e Geologia, Unidade de Modelação e Optimização de Sistemas Energéticos, Departamento de Engenharia Química e Biológica, Instituto Superior Técnico – sequence: 2 givenname: Pedro M. surname: Castro fullname: Castro, Pedro M. email: pedro.castro@ineti.pt organization: Laboratório Nacional de Energia e Geologia, Unidade de Modelação e Optimização de Sistemas Energéticos – sequence: 3 givenname: Henrique A. surname: Matos fullname: Matos, Henrique A. organization: Departamento de Engenharia Química e Biológica, Instituto Superior Técnico
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Snippet	This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in...
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SubjectTerms	Approximation Computer Science Costs Engineering Heat exchangers Linear programming Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Maximization Operations Research/Decision Theory Optimization Polynomials Production planning Programming Real Functions Studies Transformations Variables
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Title	Multi-parametric disaggregation technique for global optimization of polynomial programming problems
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