Z-tensors and complementarity problems
By M. Seethharama Gowda, Ziyan Luo, Liqun Qi, N. Xiu. 2015
64 citations recorded by the source corpus.
Tensors are multidimensional analogs of matrices. Z-tensors are tensors with non-positive off-diagonal entries. In this paper, we consider tensor complementarity problems associated with Z-tensors and describe various equivalent conditions for a Z-tensor to have the Q-property. These conditions/properties include the strong M-tensor property, the S-property, positive stable property, strict semi-monotonicity property, etc. Based on degree-theoretic ideas, we prove some refined results for even ordered tensors. We show, by an example, that a tensor complementarity problem corresponding to a strong M-tensor may not have a unique solution. A sufficient and easily check-able condition for a strong M-tensor to have unique complementarity solutions is also established.
Subfields: Computational Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/bbc56c3b7ab1bb6bcc658d6677f60456aebd05e8
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In Computational Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Polynomial complementarity problems (2016, background): “, [1], [2], [8], [13], [16], [17], and [18] and the references therein.”
- The Sparse Solution to $\mathcal{KS}$-Tensor Complementarity Problems (2022, unknown): “Recently, many kinds of TCP with different structured tensors have been studied, such as the Z-tensor [13], the positive-definite tensor [14], the P-tensor, the strong Ptensor [15] and the copositive tensor [16].”