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arXiv · 1508.00069

Properties of Solution set of Tensor Complementarity Problem

Yisheng Song·Gaohang Yu
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Abstract

The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonlinear complementarity problem. In this paper, it is proved that a tensor is an S-tensor if and only if the tensor complementarity problem is feasible, and each Q-tensor is an S-tensor. Furthermore, the boundedness of solution set of the tensor complementarity problem is equivalent to the uniqueness of solution for such a problem with zero vector. For the tensor complementarity problem with a strictly semi-positive tensor, we proved the global upper bounds for solution of such a problem. In particular, the upper bounds keep in close contact with the smallest Pareto $H-$($Z-$)eigenvalue.

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Yisheng Song, Gaohang Yu. 2015-08-01. Properties of Solution set of Tensor Complementarity Problem. https://doi.org/10.1007/s10957-016-0907-0

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