期刊
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
卷 176, 期 2, 页码 289-305出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-017-1212-2
关键词
Structured tensor; Tensor complementarity problems; Spectral radius; Operator norms; Upper and lower bounds
资金
- National Natural Science Foundation of P.R. China [11571095, 11601134, 11701154]
In this paper, one of our main purposes is to prove the boundedness of the solution set of tensor complementarity problems such that the specific bounds depend only on the structural properties of such a tensor. To achieve this purpose, firstly, we prove that this class of structured tensors is strictly semi-positive. Subsequently, the strictly lower and upper bounds of operator norms are given for two positively homogeneous operators. Finally, with the help of the above upper bounds, we show that the solution set of tensor complementarity problems has the strictly lower bound. Furthermore, the upper bounds of spectral radius are obtained, which depends only on the principal diagonal entries of tensors.
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