Exceptionally regular tensors and tensor complementarity problems
Exceptionally regular tensors and tensor complementarity problems
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DOI：
10.1080/10556788.2016.1180386
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发表时间：
2015-08
影响因子：
2.2
通讯作者：
Yong Wang;Zhenghai Huang;Xue Bai
中科院分区：
文献类型：
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作者：
Yong Wang;Zhenghai Huang;Xue Bai
近年来，许多结构张量被定义，并在文献中讨论了它们的性质。在本文中，我们引入了一类新的结构张量，称为异常正则（ER）张量，这是相关的张量互补问题（TCP）。我们证明了这类张量是一个广泛的张量类，它包括许多重要的结构张量作为它的特例。通过构造两个例子，我们证明了一个ER张量可以是，但不总是，一个R张量。我们还证明了在半正张量类中，ER-张量类与R-张量类重合。特别是，我们考虑TCP与ER张量，并证明其解集是非空的和紧的。此外，我们还得到了具有R-张量或-张量的TCP的解集是非空的和紧的。
Recently, many structured tensors are defined and their properties are discussed in the literature. In this paper, we introduce a new class of structured tensors, called exceptionally regular (ER) tensor, which is relevant to the tensor complementarity problem (TCP). We show that this class of tensors is a wide class of tensors which includes many important structured tensors as its special cases. By constructing two examples, we demonstrate that an ER-tensor can be, but not always, an R-tensor. We also show that within the class of the semi-positive tensors, the class of ER-tensors coincides with the class of R-tensors. In particular, we consider the TCP with an ER-tensor and show that its solution set is nonempty and compact. In addition, we also obtain that the solution sets of the TCP with an R-tensor or a -tensor are nonempty and compact.