Milan Hladík. On transformations in interval linear programming: just be careful!. In Proceedings of the 14th International Conference on Strategic Management and its support by Information Systems 2021, pp. 84–91, VŠB - Technical University of Ostrava, Ostrava, 2021.
We deal with linear programming problems the input data of which are uncertain. The only information we have about the uncertainty are the lower and upper bounds on the values; this yields interval enclosures of the uncertain coefficients. Interval linear programming is an established discipline with many results and open problems, too. We focus on the transformations of the constraints, which are standard in the real case, and point out the pitfalls appearing in the interval case. We will see that under general assumptions they bring fundamental changes of the problem -- either they cause infeasibility or huge overestimation.
Nonnegativity of variables was omitted in Proposition 1.
@inProceedings{Hla2021a,
author = "Milan Hlad\'{\i}k",
editor = "Radek N\v{e}mec and Lucie Chytilov\'{a}",
title = "On transformations in interval linear programming: just be careful!",
booktitle = "Proceedings of the 14th International Conference on Strategic Management and its support by Information Systems 2021",
publisher = "V\v{S}B - Technical University of Ostrava",
address = "Ostrava",
pages = "84-91",
year = "2021",
isbn = "978-80-248-4521-0",
issn = "2570-5776",
url = "https://www.ekf.vsb.cz/smsis/en/proceedings/",
bib2html_dl_pdf = "https://drive.google.com/file/d/1wV66Mqrrm_uJPpFqmyREvHX0NqUHo8aO/view?usp=sharing",
bib2html_errata = "Nonnegativity of variables was omitted in Proposition 1.",
abstract = "We deal with linear programming problems the input data of which are uncertain. The only information we have about the uncertainty are the lower and upper bounds on the values; this yields interval enclosures of the uncertain coefficients. Interval linear programming is an established discipline with many results and open problems, too. We focus on the transformations of the constraints, which are standard in the real case, and point out the pitfalls appearing in the interval case. We will see that under general assumptions they bring fundamental changes of the problem -- either they cause infeasibility or huge overestimation.",
keywords = "Interval analysis; Interval matrix; Linear programming; Optimization; Uncertainty",
}
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