Milan Hladík. Interval robustness of matrix properties for the linear complementarity problem. In Proceedings of the 15th International Symposium on Operational Research SOR'19, Bled, Slovenia, September 25-27, 2019, pp. 488–493, Slovenian Society Informatika, Ljubljana, Slovenia, 2019.
We consider the linear complementarity problem with uncertain data, where uncertainty is modeled by interval ranges of possible values. Many properties of the problem (such as solvability, uniqueness, convexity, finite number of solutions etc.) are reflected by the properties of the constraint matrix. In order that the problem has desired properties even in the uncertain environment, we have to be able to check them for all possible realizations of interval data. In particular, we will discuss S-matrix, Z-matrix, copositivity, semimonotonicity, column sufficiency and R$_0$-matrix. We characterize the robust versions of these properties and also suggest several efficiently recognizable subclasses.
@inProceedings{Hla2019d,
author = "Milan Hlad\'{\i}k",
title = "Interval robustness of matrix properties for the linear complementarity problem",
editor = "Zadnik Stirn et al., L.",
booktitle = "Proceedings of the 15th International Symposium on Operational Research SOR'19, Bled, Slovenia, September 25-27, 2019",
publisher = "Slovenian Society Informatika",
address = "Ljubljana, Slovenia",
pages = "488-493",
year = "2019",
isbn = "978-961-6165-55-6",
bib2html_dl_pdf = "http://fgg-web.fgg.uni-lj.si/~/sdrobne/sor/SOR'19%20-%20Proceedings.pdf",
abstract = "We consider the linear complementarity problem with uncertain data, where uncertainty is modeled by interval ranges of possible values. Many properties of the problem (such as solvability, uniqueness, convexity, finite number of solutions etc.) are reflected by the properties of the constraint matrix. In order that the problem has desired properties even in the uncertain environment, we have to be able to check them for all possible realizations of interval data. In particular, we will discuss S-matrix, Z-matrix, copositivity, semimonotonicity, column sufficiency and R$_0$-matrix. We characterize the robust versions of these properties and also suggest several efficiently recognizable subclasses.",
keywords = "Linear complementarity; Interval analysis; Special matrices; NP-hardness.",
}
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