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Stability of the linear complementarity problem properties under interval uncertainty

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  • Milan Hladík

    (Charles University)

Abstract

We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity 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. This leads us to the robust properties of interval matrices. In particular, we will discuss S-matrix, Z-matrix, copositivity, semimonotonicity, column sufficiency, principal nondegeneracy, $$R_0$$ R 0 -matrix and R-matrix. We characterize the robust properties and also suggest efficiently recognizable subclasses.

Suggested Citation

  • Milan Hladík, 2021. "Stability of the linear complementarity problem properties under interval uncertainty," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 875-889, September.
    • Handle: RePEc:spr:cejnor:v:29:y:2021:i:3:d:10.1007_s10100-021-00745-6
    DOI: 10.1007/s10100-021-00745-6
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    References listed on IDEAS

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    1. Janez Povh & Janez Žerovnik, 2021. "On sufficient properties of sufficient matrices," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 809-822, September.
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