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Journal of Global Optimization

, Volume 55, Issue 2, pp 227–251 | Cite as

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

  • João P. Teles
  • Pedro M. Castro
  • Henrique A. Matos
Article

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.

Keywords

Polynomial Signomial Optimization Mixed-integer linear programming Parameterization 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • João P. Teles
    • 1
    • 2
  • Pedro M. Castro
    • 1
  • Henrique A. Matos
    • 2
  1. 1.Laboratório Nacional de Energia e GeologiaUnidade de Modelação e Optimização de Sistemas EnergéticosLisboaPortugal
  2. 2.Departamento de Engenharia Química e BiológicaInstituto Superior TécnicoLisboaPortugal

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