Milan Hladík. How to determine basis stability in interval linear programming. Optim. Lett., 8(1):375–389, 2014.
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Interval linear programming (ILP) was introduced in order to deal with linear programming problems with uncertainties that are modelled by ranges of admissible values. Basic tasks in ILP such as calculating the optimal value bounds or set of all possible solutions may be computationally very expensive. However, if some basis stability criterion holds true then the problems becomes much more easy to solve. In this paper, we propose a method for testing basis stability. Even though the method is exponential in the worst case (not surprisingly due to NP-hardness of the problem), it is fast in many cases.
@article{Hla2014a,
author = "Milan Hlad\'{\i}k",
title = "How to determine basis stability in interval linear programming",
journal = "Optim. Lett.",
fjournal = "Optimization Letters",
volume = "8",
number = "1",
pages = "375-389",
year = "2014",
doi = "10.1007/s11590-012-0589-y",
issn = "1862-4472",
url = "https://doi.org/10.1007/s11590-012-0589-y",
bib2html_dl_html = "https://link.springer.com/article/10.1007%2Fs11590-012-0589-y",
bib2html_dl_pdf = "https://rdcu.be/cnoWy",
abstract = "Interval linear programming (ILP) was introduced in order to deal with linear programming problems with uncertainties that are modelled by ranges of admissible values. Basic tasks in ILP such as calculating the optimal value bounds or set of all possible solutions may be computationally very expensive. However, if some basis stability criterion holds true then the problems becomes much more easy to solve. In this paper, we propose a method for testing basis stability. Even though the method is exponential in the worst case (not surprisingly due to NP-hardness of the problem), it is fast in many cases.",
keywords = "Linear programming, Linear interval systems, Interval analysis, Basis stability",
}
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