Complementarity problems over a hypermatrix (tensor) set |
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Authors: | Mohamed A Tawhid Saeed Rahmati |
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Institution: | 1.Department of Mathematics and Statistics, Faculty of Science,Thompson Rivers University,Kamloops,Canada;2.Department of Mathematics and Computer Science, Faculty of Science,Alexandria University,Moharam Bey, Alexandria,Egypt |
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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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