Abstract
In this chapter, two algorithms for the exact explicit solution of mp-(MI)LPs under global uncertainty are presented. The algorithms comprise of two key steps: (i) analytical solution of the problem’s KKT system with the uncertain parameters and the integer variables treated as symbols using \(Gr\ddot{o}bner\) Bases and (ii) the computation of the related possibly non-convex and discontinuous CRs using Cylindrical Algebraic Decompositions on the parametric space. Problems related to process synthesis and scheduling highlight the potential of the proposed work while for the first time the functional nature of the explicit solution is theoretically characterised and proven.
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Notes
- 1.
Parts of this chapter have been reproduced with permission from: https://doi.org/10.1016/j.compchemeng.2018.04.015; https://doi.org/10.1002/aic.15755.
- 2.
Details about the related case study and its explicit solution can be found in Charitopoulos et al. [30].
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Charitopoulos, V.M. (2020). Multi-parametric Linear and Mixed Integer Linear Programming Under Global Uncertainty. In: Uncertainty-aware Integration of Control with Process Operations and Multi-parametric Programming Under Global Uncertainty. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-38137-0_3
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