Exceptionally regular tensors and tensor complementarity problems. (3rd July 2016)

• Record Type: Journal Article
• Authors: Wang, Yong; Huang, Zheng-Hai; Bai, Xue-Li
• Is Part Of: Optimization methods and software. Volume 31:Number 4(2016)
• Page Start: 815
• Page End: 828
• Publication Date: 2016-07-03
• Subjects: tensor complementarity problem -- exceptionally regular tensor -- weak P-tensor -- R-tensor; 90C33 -- 65K10 -- 15A18 -- 15A69 -- 65F15 -- 65F10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1180386
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : 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.