Higher Order Correlation Analysis for Multi-View Learning
Joint with L. Wang and Zequn Zheng, Pacific Journal of Optimization vol. 19, no. 2, 237-255, 2023.

Homogenization for polynomial optimization with unbounded sets
Joint with L. Huang and Y. Yuan, Mathematical Programming 200(1), 105--145, 2023.

Dehomogenization for Completely Positive Tensors
Joint with J. Nie, X. Tand, Z. Yang and S. Zhong, Numerical Algebra, Control and Optimization vol. 13, no. 2, 340-363, 2023.

Generalized Truncated Moment Problems with Unbounded Sets
Joint with L. Huang and Y. Yuan, Journal of Scientific Computing 95, 15 (2023).

Loss Functions for Finite Sets
Joint with S. Zhong, Computational Optimization and Applications 84, 421-447, 2023.

Distributionally Robust Optimization with Moment Ambiguity Sets
Joint with L. Yang, S. Zhong and G. Zhou, Journal of Scientific Computing 94, 12(2023).

Convex generalized Nash equilibrium problems and polynomial optimization
Joint with X. Tang, Mathematical Programming 198, 1485-1518, 2023.

Separability of Hermitian tensors and PSD decompositions
Joint with M. Dressler and Z. Yang, Linear and Multilinear Algebra , vol. 70, no. 21, 6581-6608, 2022.

The Saddle Point Problem of Polynomials
Joint with Z. Yang and G. Zhou, Foundations of Computational Mathematics 22, 1133--1169, 2022.

Learning Diagonal Gaussian Mixture Models and Incomplete Tensor Decompositions
Joint with B. Guo and Z. Yang, Vietnam Journal of Mathematics, 50(2), 421-446, 2022.

A Lagrange Multiplier Expression Method for Bilevel Polynomial Optimization
Joint with L. Wang, J. Ye and S. Zhong, SIAM Journal on Optimization, 31(3), 2368-2395, 2021.

The Gauss-Seidel Method for Generalized Nash Equilibrium Problems of Polynomials
Joint with X. Tang and L. Xu, Computational Optimization and Applications 78(2), pp. 529-557, 2021.

Stochastic Polynomial Optimization
Joint with L. Yang and S. Zhong, Optimization Methods and Software 35(2), pp. 329-347, 2020.

Hermitian Tensor Decompositions
Joint with Z. Yang, SIAM Journal on Matrix Analysis and Applications 41(3), pp. 1115-1144, 2020.

A Matrix Positivstellensatz with Lifting Polynomials
Joint with I. Klep, SIAM Journal on Optimization 30(1), 240-261, 2020.

Stochastic Polynomial Optimization
Joint with L. Yang, S. Zhong, Optimization Methods and Software, Vol. 35, no. 2, 329-347, 2020.

Tight relaxations for polynomial optimization and Lagrange multiplier expressions
Mathematical Programming, Vol. 178, No. 1-2, pp. 1-37, 2019.

Completely positive binary tensors
Joint with J. Fan, A. Zhou, Mathematics of Operations Research, Vol. 44, no. 3, 1087-1100, 2019.

Hankel tensor decompositions and ranks
Joint with K. Ye, SIAM Journal on Matrix Analysis and Applications, Vol. 40, No. 2, pp. 486-516, 2019.

A complete semidefinite algorithm for detecting copositive matrices and tensors
Joint with Z. Yang, X. Zhang, SIAM Journal on Optimization 28(4), 2902-2921, 2018.

Real eigenvalues of nonsymmetric tensors
Joint with X. Zhang, Computational Optimization and Applications 70(1), 1-32, 2018.

Tensor Eigenvalue Complementarity Problems
Joint with J. Fan, A. Zhou, Mathematical Pogramming, Ser. A, 170(2): 507-539, 2018.

Low Rank Symmetric Tensor Approximations
SIAM Journal on Matrix Analysis and Applications, Vol. 38, No. 4, pp. 1517-1540, 2017.
(The Matlab code is here).

Symmetric Tensor Nuclear Norms
SIAM Journal on Applied Algebra and Geometry, Vol. 1, No. 1, pp. 599-625, 2017.

Bilevel Polynomial Programs and Semidefinite Relaxation Methods
Joint with L. Wang, J. Ye, SIAM Journal on Optimization, Vol. 27, No. 3, pp. 1728-1757, 2017.

Generating Polynomials and Symmetric Tensor Decompositions
Foundations of Computational Mathematics, Vol. 17, No. 2, pp. 423-465, 2017.
(The Matlab code is here).

Positive Maps and Separable Matrices
Joint with X. Zhang, SIAM Journal on Optimization, Vol. 26, No. 2, pp. 1236-1256, 2016

Linear Optimization with Cones of Moments and Nonnegative Polynomials
Mathematical Programming, Ser. B, 153(1): 247-274, 2015.

The Hierarchy of Local Minimums in Polynomial Optimization
Mathematical Programming, Ser. B, Vol. 151, No.2, pp. 555-583, 2015.

All Real Eigenvalues of Symmetric Tensors.
Joint with C. Cui and Y. Dai. SIAM Jounral on Matrix Analysis and Applications, Vol. 35, No. 4, pp. 1582-1601, 2014.
(The Matlab code is here).

Semidefinite Relaxations for Best Rank-1 Tensor Approximations
Joint with L. Wang. SIAM Jounral on Matrix Analysis and Applications, Vol. 35, No. 3, pp. 1155-1179, 2014.
(The Matlab code is here).

The A-Truncated K-Moment Problem
Foundations of Computational Mathematics, Vol. 14, No. 6, pp. 1243-1276, 2014.

Optimality Conditions and Finite Convergence of Lasserre's Hierarchy
Mathematical Programming, Ser. A, Vol 146, No. 1-2, pp. 97-121, 2014.

Polynomial Optimization with Real Varieties
SIAM Journal on Optimization, Vol 23, No.3, pp. 1634-1646, 2013.

Certifying Convergence of Lasserre's Hierarchy via Flat Truncation
Mathematical Programming, Ser. A, Vol 142, No. 1-2, pp. 485-510, 2013.

An Approximation Bound Analysis for Lasserre's Relaxation in Multivariate Polynomial Optimization
Journal of the Operations Research Society of China, Vol. 1, No. 3, pp. 313-332, 2013.

A Semidefinite Approach for Truncated K-Moment Problem
Joint with J.W. Helton, Foundations of Computational Mathematics, Vol. 12, No. 6, pp. 851-881, 2012.

An Exact Jacobian SDP Relaxation for Polynomial Optimization
Mathematical Programming, Ser. A, Vol. 137, No. 1-2, pp. 225-255, 2013.

The truncated moment problem via homogenization and flat extensions
Joint with L. Fialkow, Journal of Functional Analysis 263 (2012), no. 6, 1682-1700.

Regularization Methods for SDP Relaxations in Large Scale Polynomial Optimization
Joint with L. Wang, SIAM Journal On Optimization, Vol. 22, No. 2, pp. 408-428, 2012. (The Matlab code is here).

First Order Conditions for Semidefinite Representations of Convex Sets Defined by Rational or Singular Polynomials
Mathematical Programming, Ser. A, Vol. 131, No. 1, pp. 1-36, 2012.

Discriminants and Nonnegative Polynomials
Journal of Symbolic Computation, Vol. 47, No. 2, pp. 167-191, 2012.

Sum of squares methods for minimizing polynomial functions over spheres and hypersurfaces,
Frontiers of Mathematics in China, Vol 7, No.2, pp. 321-346, 2012.

Polynomial Matrix Inequality and Semidefinite Representation
Mathematics of Operations Research, Vol. 36, No. 3, pp. 398-415, 2011.

Positivity of Riesz Functionals and Solutions of Quadratic and Quartic Moment Problems
Joint with L. Fialkow, Journal of Functional Analysis, Vol. 258, No. 1, pp. 328-356, 2010.

The Algebraic Degree of Semidefinite Programming
Joint with K. Ranestad and B. Sturmfels, Mathematical Programming, Series A, Vol. 122, No.2, pp. 379-405, 2010.

Semidefinite Representation of Convex Sets
Joint with J.W. Helton, Mathematical Programming, Series A, Vol. 122, No.1, pp.21-64, 2010.

Bi-Quadratic Optimization over Unit Spheres and Semidefinite Programming Relaxations
Joint with C. Ling, L. Qi, and Y. Ye, SIAM Journal on Optimization, Vol. 20, No. 3, pp.1286-1310, 2010.

Matrix cubes parametrized by eigenvalues
Joint with B. Sturmfels, SIAM Journal on Matrix Analysis and Applications, Vol. 31, No. 2, pp. 755-766, 2009.

Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets
Joint with J.W. Helton, SIAM Journal on Optimization, Vol. 20, No.2, pp. 759-791, 2009.

Sum of squares method for sensor network localization
Computational Optimization and Applications, Vol.43, No. 2 (2009), pp. 151-179.

Algebraic Degree of Polynomial Optimization
Joint with K. Ranestad, SIAM Journal on Optimization, Vol. 20, No. 1, pp. 485-502, 2009.

Sparse SOS relaxations for minimizing functions that are summations of small polynomials
Join with J. Demmel, SIAM Journal On Optimization, Vol. 19, No. 4, pp. 1534-1558 (2008).

Semidefinite Relaxation Bounds for Indefinite Homogeneous Quadratic Optimization
Joint with S. He, Z. Luo, and S. Zhang, SIAM Journal on Optimization, Vol. 19, No.2, pp. 503-523, 2008.

Global minimization of rational functions and the nearest GCDs
Joint with J. Demmel and M. Gu, Journal of Global Optimization, Vol. 40 (2008), No.4, 697-718.

On the complexity of putinar's positivstellensatz
Joint with M. Schweighofer, Journal of Complexity 23(2007), pp.135-150.

Representations of positive polynomials on non-compact semialgebraic sets via KKT ideals
Joint with J. Demmel and V. Powers, Journal of Pure and Applied Algebra, Vol. 209, No. 1, pp. 189-200, 2007.

Minimizing polynomials via sum of squares over the gradient ideal
Joint with J. Demmel and B. Sturmfels, Mathematical Programming, Series A, Vol. 106 (2006), No. 3, pp. 587-606.

Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares
Joint with J. Demmel, Journal of Global Optimization, Vol. 33(2005), pp. 511-525.