相关论文: A continuation method for tensor complementarity p…
The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a…
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…
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…
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…
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…
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 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…
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 concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…
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 this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose…
We are concerned with the tensor equations whose coefficient tensor is an M-tensor. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend…
In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose,…
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.…
Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive…
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…
In this article we introduce column adequate tensor in the context of tensor complementarity problem and consider some important properties. The tensor complementarity problem is a class of nonlinear complematarity problems with the…
Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…
The main purpose of this note is to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as, symmetric positive definite tensors and copositive tensors, we derive the existence theorems on a…
We prove the existence of positive solutions for a class of semipositone problem with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.