Milan Hladík and Miroslav Rada. The horizontal linear complementarity problem and robustness of the related matrix classes. In B. Dorronsoro and others, editors, Optimization and Learning, CCIS, pp. 350–360, Springer, Cham, 2021.
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We consider the horizontal linear complementarity problem and we assume that the input data have the form of intervals, representing the range of possible values. For the classical linear complementarity problem, there are known various matrix classes that identify interesting properties of the problem (such as solvability, uniqueness, convexity, finite number of solutions or boundedness). Our aim is to characterize the robust version of these properties, that is, to check them for all possible realizations of interval data. We address successively the following matrix classes: nonnegative matrices, Z-matrices, semimonotone matrices, column sufficient matrices, principally nondegenerate matrices, $R_0$-matrices and R-matrices. The reduction of the horizontal linear complementarity problem to the classical one, however, brings complicated dependencies between interval parameters, resulting in some cases to higher computational complexity.
@inCollection{HlaRad2021a,
author = "Milan Hlad\'{\i}k and Miroslav Rada",
title = "The horizontal linear complementarity problem and robustness of the related matrix classes",
editor = "B. Dorronsoro and others",
feditor = "Dorronsoro, Bernab{\'e} and Amodeo, Lionel and Pavone, Mario and Ruiz, Patricia",
booktitle = "Optimization and Learning",
fbooktitle = "Optimization and Learning. OLA 2021.",
publisher = "Springer",
address = "Cham",
series = "CCIS",
fseries = "Communications in Computer and Information Science",
volume = "1443",
pages = "350-360",
year = "2021",
doi = "10.1007/978-3-030-85672-4_26",
isbn = "978-3-030-85672-4",
url = "https://doi.org/10.1007/978-3-030-85672-4_26",
bib2html_dl_html = "https://link.springer.com/chapter/10.1007/978-3-030-85672-4_26",
abstract = "We consider the horizontal linear complementarity problem and we assume that the input data have the form of intervals, representing the range of possible values. For the classical linear complementarity problem, there are known various matrix classes that identify interesting properties of the problem (such as solvability, uniqueness, convexity, finite number of solutions or boundedness). Our aim is to characterize the robust version of these properties, that is, to check them for all possible realizations of interval data. We address successively the following matrix classes: nonnegative matrices, Z-matrices, semimonotone matrices, column sufficient matrices, principally nondegenerate matrices, $R_0$-matrices and R-matrices. The reduction of the horizontal linear complementarity problem to the classical one, however, brings complicated dependencies between interval parameters, resulting in some cases to higher computational complexity.",
keywords = "Linear complementarity;Interval analysis; Special matrices; NP-hardness",
}
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