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Necessary and sufficient conditions for the existence of complementary solutions and characterizations of the matrix classesQ andQ 0

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Abstract

We simplify a result by Mangasarian on the existence of solutions to the linear complementarity problem. The simplified condition gives a new geometric interpretation of the result. When used to characterize the matrix classesQ andQ 0, our condition suggests a finitely checkable sufficient condition forP andP 0.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332-0205, Atlanta, GA, USA

    Faiz A. Al-Khayyal

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  1. Faiz A. Al-Khayyal
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This work was supported in part by the Office of Naval Research under Contract No. N00014-86-K-0173, and by general research development funds provided by the Georgia Institute of Technology.

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Al-Khayyal, F.A. Necessary and sufficient conditions for the existence of complementary solutions and characterizations of the matrix classesQ andQ 0 . Mathematical Programming 51, 247–255 (1991). https://doi.org/10.1007/BF01586936

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  • DOI: https://doi.org/10.1007/BF01586936

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