Elif Garajová, Miroslav Rada, and Milan Hladík. Bilevel linear programming under interval uncertainty. In 39th International Conference on Mathematical Methods in Economics 2021. Conference Proceedings, pp. 123–128, Czech University of Life Sciences Prague, 2021.
Bilevel linear programming provides a suitable mathematical model for many practical optimization problems. Since the real-world data are often inaccurate or uncertain, we consider the model under interval uncertainty, in which only the lower and upper bounds on the input data are available and we assume that the uncertain coefficients can be perturbed independently within the given intervals. Building on the theory of interval optimization and bilevel linear programming, we study the basic properties of bilevel interval linear programs from both a theoretical and a computational point of view. In our study, we focus on the main problems solved in interval optimization, such as computing the range of optimal values, checking the existence of feasible and optimal solutions and testing unboundedness of a scenario in the interval program.
@InProceedings{GarRad2021a,
author = "Elif Garajov\'{a} and Miroslav Rada and Milan Hlad\'{\i}k",
title = "Bilevel linear programming under interval uncertainty",
editor = "Robert Hlavat\'{y}",
booktitle = "39th International Conference on Mathematical Methods in Economics 2021. Conference Proceedings",
pages = "123-128",
year = "2021",
publisher = "Czech University of Life Sciences Prague",
isbn = "978-80-213-3126-6",
url = "https://mme2021.v2.czu.cz/dl/99363?lang=en",
bib2html_dl_pdf = "https://mme2021.v2.czu.cz/dl/99363?lang=en",
abstract = "Bilevel linear programming provides a suitable mathematical model for many practical optimization problems. Since the real-world data are often inaccurate or uncertain, we consider the model under interval uncertainty, in which only the lower and upper bounds on the input data are available and we assume that the uncertain coefficients can be perturbed independently within the given intervals. Building on the theory of interval optimization and bilevel linear programming, we study the basic properties of bilevel interval linear programs from both a theoretical and a computational point of view. In our study, we focus on the main problems solved in interval optimization, such as computing the range of optimal values, checking the existence of feasible and optimal solutions and testing unboundedness of a scenario in the interval program.",
keywords = "Bilevel programming; Interval uncertainty; Optimality",
}
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