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

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  • João Teles
  • Pedro Castro
  • Henrique Matos

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. Copyright Springer Science+Business Media, LLC. 2013

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  • João Teles & Pedro Castro & Henrique Matos, 2013. "Multi-parametric disaggregation technique for global optimization of polynomial programming problems," Journal of Global Optimization, Springer, vol. 55(2), pages 227-251, February.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:2:p:227-251
    DOI: 10.1007/s10898-011-9809-8
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    References listed on IDEAS

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    1. Tsai, Jung-Fa & Lin, Ming-Hua & Hu, Yi-Chung, 2007. "On generalized geometric programming problems with non-positive variables," European Journal of Operational Research, Elsevier, vol. 178(1), pages 10-19, April.
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    Cited by:

    1. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2016. "New multi-commodity flow formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 66(4), pages 669-710, December.
    2. Jianhui Xie & Qiwei Xie & Yongjun Li & Liang Liang, 2021. "Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique," Annals of Operations Research, Springer, vol. 304(1), pages 453-480, September.
    3. Enayati, Shakiba & Özaltın, Osman Y., 2020. "Optimal influenza vaccine distribution with equity," European Journal of Operational Research, Elsevier, vol. 283(2), pages 714-725.
    4. Pedro Castro & Ignacio Grossmann, 2014. "Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems," Journal of Global Optimization, Springer, vol. 59(2), pages 277-306, July.
    5. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.
    6. Xin Cheng & Xiang Li, 2022. "Discretization and global optimization for mixed integer bilinear programming," Journal of Global Optimization, Springer, vol. 84(4), pages 843-867, December.
    7. Tiago Andrade & Fabricio Oliveira & Silvio Hamacher & Andrew Eberhard, 2019. "Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming," Journal of Global Optimization, Springer, vol. 73(4), pages 701-722, April.

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