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

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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.

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Authors and Affiliations

  1. Laboratório Nacional de Energia e Geologia, Unidade de Modelação e Optimização de Sistemas Energéticos, 1649-038, Lisboa, Portugal

    João P. Teles & Pedro M. Castro

  2. Departamento de Engenharia Química e Biológica, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

    João P. Teles & Henrique A. Matos

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  1. João P. Teles
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  2. Pedro M. Castro
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  3. Henrique A. Matos
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Correspondence to Pedro M. Castro.

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Teles, J.P., Castro, P.M. & Matos, H.A. Multi-parametric disaggregation technique for global optimization of polynomial programming problems. J Glob Optim 55, 227–251 (2013). https://doi.org/10.1007/s10898-011-9809-8

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  • DOI: https://doi.org/10.1007/s10898-011-9809-8

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