Milan Hladík. On strong optimality of interval linear programming. Optim. Lett., 11(7):1459–1468, 2017.
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We consider a linear programming problem with interval data. We discuss the problem of checking whether a given solution is optimal for each realization of interval data. This problem was studied for particular forms of linear programming problems. Herein, we extend the results to a general model and simplify the overall approach. Moreover, we inspect computational complexity, too. Eventually, we investigate a related optimality concept of semi-strong optimality, showing its characterization and complexity.
In (4), matrices A and C should take a slightly different form involving the sign vector s.
@article{Hla2017d,
author = "Milan Hlad\'{\i}k",
title = "On strong optimality of interval linear programming",
journal = "Optim. Lett.",
fjournal = "Optimization Letters",
volume = "11",
number = "7",
pages = "1459-1468",
year = "2017",
doi = "10.1007/s11590-016-1088-3",
issn = "1862-4480",
bib2html_dl_html = "https://doi.org/10.1007/s11590-016-1088-3",
bib2html_dl_pdf = "http://rdcu.be/lsig",
bib2html_errata = "In (4), matrices A and C should take a slightly different form involving the sign vector s.",
abstract = "We consider a linear programming problem with interval data. We discuss the problem of checking whether a given solution is optimal for each realization of interval data. This problem was studied for particular forms of linear programming problems. Herein, we extend the results to a general model and simplify the overall approach. Moreover, we inspect computational complexity, too. Eventually, we investigate a related optimality concept of semi-strong optimality, showing its characterization and complexity.",
keywords = "Linear programming; Interval analysis; Uncertainty modeling",
}
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