Strictly semi-positive tensors and the boundedness of tensor complementarity problems
نویسندگان
چکیده
منابع مشابه
Strictly semi-positive tensors and the boundedness of tensor complementarity problems
In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all H+(Z+)-eigenvalues of each principal sub-tensor are positive. We define two new constants associated with H+(Z+)-eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establ...
متن کاملTensor Complementarity Problem and Semi-positive Tensors
In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is showed that a real symmetric tensor is a (strictly) semi-positi...
متن کاملPositive-Definite Tensors to Nonlinear Complementarity Problems
The main purpose of this paper 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 solution of these kinds of nonlinear complementarity problems. We prove that a unique solution of the NCP exists under the condition of diagonalizable tensors.
متن کاملHigher-degree eigenvalue complementarity problems for tensors
In this paper, we introduce a unified framework of Tensor Higher-Degree EigenvalueComplementarity Problem (THDEiCP),which goes beyond the framework of the typical Quadratic Eigenvalue Complementarity Problem for matrices. First, we study some topological properties of higher-degree cone eigenvalues of tensors. Based upon the symmetry assumptions on the underlying tensors, we then reformulate TH...
متن کاملProperties of Tensor Complementarity Problem and Some Classes of Structured Tensors
This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor A such that the tensor complementarity problem (q,A): finding x ∈ R such that x ≥ 0,q+Axm−1 ≥ 0, and x⊤(q+Axm−1) = 0, has a solution for each vector q ∈ Rn. Several subclasses of Q-tensors are given: P-tensors, R-tensors, strictly semi-positive tensors and semi-positive R0-tensors. We prove that a nonnegative ten...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Optimization Letters
سال: 2016
ISSN: 1862-4472,1862-4480
DOI: 10.1007/s11590-016-1104-7