相关论文: B tensors and tensor complementarity problems

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…

Our purpose is to investigate the local boundedness, the upper semicontinuity, and the stability of the solution map of tensor complementarity problems. To do this, we focus on the set of R$_0$--tensors and show that this set plays an…

In this paper, we prove that all H$^+$(Z$^+$)-eigenvalues of each principal sub-tensor of a strictly semi-positive tensor are positive. We define two new constants associated with H$^+$(Z$^+$)eigenvalues of a strictly semi-positive tensor.…

In this paper, we introduce set-valued tensor complementarity problem where the elements of the involved tensors are defined based on a set-valued mapping. We study several properties of the solution set under the framework of set-valued…

It is easily checkable if a given tensor is a B tensor, or a B$_0$ tensor or not. In this paper, we show that a symmetric B tensor can always be decomposed to the sum of a strictly diagonally dominated symmetric M tensor and several…

In this paper, we mainly focus on the existence and uniqueness of the vertical tensor complementarity problem. Firstly, combining the generalized-order linear complementarity problem with the tensor complementarity problem, the vertical…

In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the…

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 tensor, which is relevant to the tensor…

The tensor complementarity problem $(\q, \mathcal{A})$ is to $$\mbox{ find } \x \in \mathbb{R}^n\mbox{ such that }\x \geq \0, \q + \mathcal{A}\x^{m-1} \geq \0, \mbox{ and }\x^\top (\q + \mathcal{A}\x^{m-1}) = 0.$$ We prove that a real…

The main purpose of this paper is devoted to an introduction of the stochastic tensor complementarity problem. We consider the expected residual minimization formulation of the stochastic tensor complementarity problem. We show that the…

In this paper, we introduce semi-infinite tensor complementarity problem to provide an approach for considering a more realistic situation of the problem. We prove the necessary and sufficient conditions for the existence of the solution…

This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor $\mathcal{A}$ such that the tensor complementarity problem $(\q, \mathcal{A})$: $$\mbox{ finding } \x \in \mathbb{R}^n\mbox{ such that }\x \geq \0, \q +…

Tensors are multidimensional analogs of matrices. In this paper, based on degree-theoretic ideas, we study homogeneous nonlinear complementarity problems induced by tensors. By specializing this to $Z$-tensors (which are tensors with…

In this paper, we give a further study on $B$-tensors and introduce doubly $B$-tensors that contain $B$-tensors. We show that they have similar properties, including their decompositions and strong relationship with strictly (doubly)…

In this article, we introduce the class $B$-Nekrasov tensor in the context of tensor complementarity problem. We study some tensor theoretic properties. We show that the class of B-Nekrasov tensor contains the class of Nekrasov $Z$-tensor…

This paper systematically investigates the properties and characterization of interval B-tensors and interval double B-tensors. We propose verifiable necessary and sufficient conditions that allow for determining whether an entire interval…

In this paper, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors, give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with B-tensors and positive definite tensors…

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…

We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…

This paper investigates the convexity of the solution set of the linear complementarity problems over tensor spaces (TLCPs). We introduce the notion of a $T$-column sufficient tensor and study its properties and relationships with several…