Jana Novotná, Milan Hladík, and Tomáš Masařík. Duality gap in interval linear programming. J. Optim. Theory Appl., 184(2):565–580, 2020.
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This paper deals with the problem of linear programming with inexact data represented by real intervals. We introduce the concept of duality gap to interval linear programming. We give characterizations of strongly and weakly zero duality gap in interval linear programming and its special case where the matrix of coefficients is real. We show computational complexity of testing weakly- and strongly zero duality gap for commonly used types of interval linear programming.
Page 569, last line: should be $\overline{A}^T$ instead of $\underline{A}^T$. Page 570, Cor. 2.4(iii): remove the claim on A.
@article{NovHla2020a,
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",
journal = "J. Optim. Theory Appl.",
fjournal = "Journal of Optimization Theory and Applications",
volume = "184",
number = "2",
pages = "565-580",
year = "2020",
doi = "10.1007/s10957-019-01610-y",
issn = "1573-2878",
url = "https://doi.org/10.1007/s10957-019-01610-y",
bib2html_dl_html = "https://link.springer.com/article/10.1007/s10957-019-01610-y",
bib2html_dl_pdf = "https://rdcu.be/cno0C",
bib2html_errata = "Page 569, last line: should be $\overline{A}^T$ instead of $\underline{A}^T$. Page 570, Cor. 2.4(iii): remove the claim on A.",
abstract = "This paper deals with the problem of linear programming with inexact data represented by real intervals. We introduce the concept of duality gap to interval linear programming. We give characterizations of strongly and weakly zero duality gap in interval linear programming and its special case where the matrix of coefficients is real. We show computational complexity of testing weakly- and strongly zero duality gap for commonly used types of interval linear programming.",
keywords = "Interval analysis; Linear programming; Interval linear programming; Duality gap; Computational complexity",
}
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