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The Horizontal Linear Complementarity Problem and Robustness of the Related Matrix Classes

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Optimization and Learning (OLA 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1443))

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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.

Supported by the Czech Science Foundation Grants P403-18-04735S (M. Hladík) and P403-20-17529S (M. Rada).

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Applied Mathematics, Charles University, Malostranské nám. 25, 11800, Prague, Czech Republic

    Milan Hladík

  2. Faculty of Informatics and Statistics, Department of Econometrics, University of Economics, W. Churchill’s Sq. 4, 130 67, Prague, Czech Republic

    Miroslav Rada

Authors
  1. Milan Hladík
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  2. Miroslav Rada
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Correspondence to Milan Hladík .

Editor information

Editors and Affiliations

  1. University of Cádiz, Cádiz, Spain

    Bernabé Dorronsoro

  2. University of Technology of Troyes, Troyes, France

    Lionel Amodeo

  3. University of Catania, Catania, Italy

    Mario Pavone

  4. University of Cádiz, Cádiz, Spain

    Patricia Ruiz

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Hladík, M., Rada, M. (2021). The Horizontal Linear Complementarity Problem and Robustness of the Related Matrix Classes. In: Dorronsoro, B., Amodeo, L., Pavone, M., Ruiz, P. (eds) Optimization and Learning. OLA 2021. Communications in Computer and Information Science, vol 1443. Springer, Cham. https://doi.org/10.1007/978-3-030-85672-4_26

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  • DOI: https://doi.org/10.1007/978-3-030-85672-4_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85671-7

  • Online ISBN: 978-3-030-85672-4

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