Milan Hladík and Michal Černý. First step immersion in interval linear programming with linear dependencies. Bull. Iranian Math. Soc., 42(7):43–53, 2016.
We consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals. Contrary to classical models, where parameters can attain any value from the interval domains independently, we study problems with linear dependencies between the parameters. We present a class of problems that are easily solved by reduction to the classical case. In contrast, we also show a class of problems with very simple dependencies, which appear to be hard to deal with. We also point out some interesting open problems.
@article{HlaCer2016a,
author = "Milan Hlad\'{\i}k and Michal {\v{C}}ern\'{y}",
title = "First step immersion in interval linear programming with linear dependencies",
journal = "Bull. Iranian Math. Soc.",
fjournal = "Bulletin of the Iranian Mathematical Society",
volume = "42",
number = "7",
pages = "43-53",
year = "2016",
issn = "1017-060X",
bib2html_dl_html = "http://bims.iranjournals.ir/article_887.html",
abstract = "We consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals. Contrary to classical models, where parameters can attain any value from the interval domains independently, we study problems with linear dependencies between the parameters. We present a class of problems that are easily solved by reduction to the classical case. In contrast, we also show a class of problems with very simple dependencies, which appear to be hard to deal with. We also point out some interesting open problems.",
keywords = "Linear programming; Interval analysis; Linear dependencies",
}
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