14 citations · 64 across the 19 of their papers we have counts for
19 papers
Deterministic Dynamic Stackelberg Games: Time-Consistent Open-Loop Solution
Yuan-Hua Ni, Liping Liu, Xinzhen Zhang
In this paper, the known deterministic linear-quadratic Stackelberg game is revisited, whose open-loop Stackelberg solution actually possesses the nature of time inconsistency. To…
Tensor factorization based method for low rank matrix completion and its application on tensor completion
Quan Yu, Xinzhen Zhang
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and t…
A smoothing proximal gradient algorithm for matrix rank minimization problem
Quan Yu, Xinzhen Zhang
In this paper, we study the low-rank matrix minimization problem, where the loss function is convex but nonsmooth and the penalty term is defined by the cardinality function. We fi…
T-Quadratic Forms and Spectral Analysis of T-Symmetric Tensors
Liqun Qi, Xinzhen Zhang
An tensor is called a T-square tensor. It arises from many applications, such as the image feature extraction problem and the multi-view clustering problem. W…
Multi-Tubal Rank of Third Order Tensor and Related Low Rank Tensor Completion Problem
Quan Yu, Xinzhen Zhang, Zheng-Hai Huang
Recently, a tensor factorization based method for a low tubal rank tensor completion problem of a third order tensor was proposed, which performed better than some existing methods…
A Low Rank Quaternion Decomposition Algorithm and Its Application in Color Image Inpainting
Yannan Chen, Liqun Qi, Xinzhen Zhang +1
In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in…
Positivity Conditions for Cubic, Quartic and Quintic Polynomials
Liqun Qi, Yisheng Song, Xinzhen Zhang
We present a necessary and sufficient condition for a cubic polynomial to be positive for all positive reals. We identify the set where the cubic polynomial is nonnegative but not…
Quaternion Matrix Optimization and The Underlying Calculus
Liqun Qi, Ziyan Luo, Qingwen Wang +1
Optimization models involving quaternion matrices are widely used in color image process and other engineering areas. These models optimize real functions of quaternion matrix vari…
Copositivity of Three-Dimensional Symmetric Tensors
Liqun Qi, Yisheng Song, Xinzhen Zhang
In this paper, we seek analytically checkable necessary and sufficient condition for copositivity of a three-dimensional symmetric tensor. We first show that for a general third or…
A Tensor Rank Theory and Maximum Full Rank Subtensors
Liqun Qi, Xinzhen Zhang, Yannan Chen
A matrix always has a full rank submatrix such that the rank of this matrix is equal to the rank of that submatrix. This property is one of the corner stones of the matrix rank the…
Triple Decomposition and Tensor Recovery of Third Order Tensors
Liqun Qi, Yannan Chen, Mayank Bakshi +1
In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We ca…
Tensor Norm, Cubic Power and Gelfand Limit
Liqun Qi, Shenglong Hu, Xinzhen Zhang +1
We establish two inequalities for the nuclear norm and the spectral norm of tensor products. The first inequality indicates that the nuclear norm of the square matrix is a matrix n…
Biquadratic Tensors, Biquadratic Decomposition and Norms of Biquadratic Tensors
Liqun Qi, Shenglong Hu, Xinzhen Zhang
Biquadratic tensors play a central role in many areas of science. Examples include elasticity tensor and Eshelby tensor in solid mechanics, and Riemann curvature tensor in relativi…
A Nash-Type Fictitious Game Framework to Time-Inconsistent Stochastic Control Problems
Yuan-Hua Ni, Binbin Si, Xinzhen Zhang
In this paper, a Nash-type fictitious game framework is introduced to handle a time-inconsistent linear-quadratic optimal control. The Nash-type game in this framework is called fi…
Calculating Entanglement Eigenvalues for Non-Symmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method
Mengshi Zhang, Xinzhen Zhang, Guyan Ni
The geometric measure of entanglement is a widely used entanglement measure for quantum pure states. The key problem of computation of the geometric measure is to calculate the ent…
A Complete Semidefinite Algorithm for Detecting Copositive Matrices and Tensors
Jiawang Nie, Zi Yang, Xinzhen Zhang
A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant…
Positive Maps and Separable Matrices
Jiawang Nie, Xinzhen Zhang
A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable i…
Real Eigenvalues of nonsymmetric tensors
Jiawang Nie, Xinzhen Zhang
This paper discusses the computation of real Z-eigenvalues and H-eigenvalues of nonsymmetric tensors. A general nonsymmetric tensor has finitely many Z-eigenvalues, while there may…
The Quantum Eigenvalue Problem and Z-Eigenvalues of Tensors
Xinzhen Zhang, Liqun Qi
The quantum eigenvalue problem arises in the study of the geometric measure of the quantum entanglement. In this paper, we convert the quantum eigenvalue problem to the Z-eigenvalu…