Elif Garajová, Milan Hladík, and Miroslav Rada. The effects of transformations on the optimal set in interval linear programming. In Proceedings of the 14th International Symposium on Operational Research SOR'17, Bled, Slovenia, September 27-29, 2017, pp. 487–492, Slovenian Society Informatika, Ljubljana, Slovenia, 2017.
Interval linear programming provides a mathematical tool for handling linear optimization problems affected by uncertainty. Contrarily to classical linear programming, the properties of interval linear programs depend on the form in which the program is given. In this paper, we study how the transformations used in linear programming - imposing non-negativity, changing equations to inequalities and vice versa - affect the optimal set of an interval program. Since the results are mostly negative in the general case, we also consider interval linear programs with a fixed coefficient matrix. For this special case, we prove that all transformations preserve the optimal solution set.
@inProceedings{GarHla2017a,
author = "Elif Garajov\'{a} and Milan Hlad\'{\i}k and Miroslav Rada",
title = "The effects of transformations on the optimal set in interval linear programming",
editor = "Zadnik Stirn et al., L.",
booktitle = "Proceedings of the 14th International Symposium on Operational Research SOR'17, Bled, Slovenia, September 27-29, 2017",
publisher = "Slovenian Society Informatika",
address = "Ljubljana, Slovenia",
pages = "487-492",
year = "2017",
isbn = "978-961-6165-50-1",
bib2html_dl_pdf = "http://fgg-web.fgg.uni-lj.si/~/sdrobne/sor/SOR'17%20-%20Proceedings.pdf",
abstract = "Interval linear programming provides a mathematical tool for handling linear optimization problems affected by uncertainty. Contrarily to classical linear programming, the properties of interval linear programs depend on the form in which the program is given. In this paper, we study how the transformations used in linear programming - imposing non-negativity, changing equations to inequalities and vice versa - affect the optimal set of an interval program.
Since the results are mostly negative in the general case, we also consider interval linear programs with a fixed coefficient matrix. For this special case, we prove that all transformations preserve the optimal solution set.",
keywords = "Interval linear programming; Optimal set; Transformations",
}
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