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Complementarity problems over a hypermatrix (tensor) set

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Abstract

A hypermatrix (tensor) complementarity problem \(\textit{HMCP}(q,\mathcal {A})\) is to find a vector \(x\in \mathbb {R}^n\) such that \(x\ge 0,~\mathcal {A}x+q\ge 0,~x^T(\mathcal {A}x+q)=0,\) for every \(q\in \mathbb {R}^n\), where \(\mathcal {A}\) is an mth order hypermatrix (tensor) (Song and Qi in J Optim Theory Appl 165(3): 854–873, 2015). Uniqueness, feasibility, and strict feasibility of the solution of a complementarity problem induced by a (compact) set of hypermatrices are characterized in terms of the hypermatrices involved.

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Acknowledgements

The authors would like to thank the referees for their insightful comments. The research of the 1st author is supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, V2C 0C8, Canada

    Mohamed A. Tawhid & Saeed Rahmati

  2. Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bey, Alexandria, 21511, Egypt

    Mohamed A. Tawhid

Authors
  1. Mohamed A. Tawhid
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  2. Saeed Rahmati
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Correspondence to Mohamed A. Tawhid.

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Tawhid, M.A., Rahmati, S. Complementarity problems over a hypermatrix (tensor) set. Optim Lett 12, 1443–1454 (2018). https://doi.org/10.1007/s11590-018-1234-1

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  • DOI: https://doi.org/10.1007/s11590-018-1234-1

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