Yisheng Song

Properties of Some Classes of Structured Tensors

In this paper, we extend some classes of structured matrices to higher-order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. The potential links of such structured tensors with optimization, nonlinear equations, nonlinear complementarity problems, variational inequalities and the non-negative tensor theory are also discussed.

Tensor 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 that 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 shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.

SOME NOTES ON ISHIKAWA ITERATION FOR MULTI-VALUED MAPPINGS

In Shahzad and Zegeye (Nonlinear Anal. 71 (2009), no. 3-4, 838{844), the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration fxng to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.

Spectral Properties of Positively Homogeneous Operators Induced by Higher Order Tensors

The Fredholm alternative type results are proved for eigenvalues (

Properties of Solution Set of Tensor Complementarity Problem

E

Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming

-eigenvalues,

A note on a paper A regularization method for the proximal point algorithm

H

Necessary and sufficient conditions for copositive tensors

-eigenvalues,

Eigenvalue analysis of constrained minimization problem for homogeneous polynomial

Z

A new sufficient condition for the strong convergence of Halpern type iterations

-eigenvalues) of a higher order tensor