Jana Novotná, Milan Hladík, and Tomáš Masařík. Duality gap in interval linear programming. In Proceedings of the 14th International Symposium on Operational Research SOR'17, Bled, Slovenia, September 27-29, 2017, pp. 501–506, Slovenian Society Informatika, Ljubljana, Slovenia, 2017.
This paper deals with the problem of linear programming with inexact data represented by real intervals. We extend the concept of duality gap (DG), the difference between the primal and its dual optimal value, into interval linear programming (ILP). We give characterizations of strongly- and weakly-zero DG in ILP and its special case where the matrix of coefficients is real. We show computational complexity of testing weakly- and strongly-zero DG for commonly used types of ILP.
@inProceedings{NovHla2017a,
author = "Jana Novotn\'{a} and Milan Hlad\'{\i}k and Tom\'{a}\v{s} Masa\v{r}\'{\i}k",
title = "Duality gap 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 = "501-506",
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 = "This paper deals with the problem of linear programming with inexact data represented by real intervals. We extend the concept of duality gap (DG), the difference between the primal and its dual optimal value, into interval linear programming (ILP). We give characterizations of strongly- and weakly-zero DG in ILP and its special case where the matrix of coefficients is real. We show computational complexity of testing weakly- and strongly-zero DG for commonly used types of ILP.",
keywords = "Interval analysis; Linear programming; Interval linear programming; Duality gap",
}
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