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Multi-parametric linear programming under global uncertainty

Charitopoulos, VM; Papageorgiou, LG; Dua, V; (2017) Multi-parametric linear programming under global uncertainty. AIChE Journal , 63 (9) pp. 3871-3895. 10.1002/aic.15755. Green open access

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Abstract

Multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush–Kuhn–Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms.

Type: Article
Title: Multi-parametric linear programming under global uncertainty
Open access status: An open access version is available from UCL Discovery
DOI: 10.1002/aic.15755
Publisher version: http://doi.org/10.1002/aic.15755
Language: English
Additional information: Copyright © 2017 The Authors This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/1554442
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