Strictly semi-positive tensors and the boundedness of tensor complementarity problems. (English) Zbl 1454.90098
Summary: In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all \(H^+(Z^+)\)-eigenvalues of each principal sub-tensor are positive. We define two new constants associated with \(H^+(Z^+)\)-eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establish upper bounds of an important quantity whose positivity is a necessary and sufficient condition for a general tensor to be a strictly semi-positive tensor. The monotonicity and boundedness of such a quantity are established too.
MSC:
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 15A69 | Multilinear algebra, tensor calculus |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
Keywords:
strictly semi-positive tensor; tensor complementarity problem; upper and lower bounds; eigenvaluesReferences:
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