Book Chapters

Tensor Eigenvalue Complementarity Problems

Joint with J. Fan, A. Zhou,Mathematical Pogramming, to appear.

Bilevel Polynomial Programs and Semidefinite Relaxation Methods

Joint with L. Wang, J. Ye,SIAM Journal on Optimization, to appear.

Generating Polynomials and Symmetric Tensor Decompositions

Foundations of Computational Mathematics, to appear.

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 Analysis263 (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, 2009.

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 Complexity23(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.

Convex Hulls of Quadratically Parameterized Sets With Quadratic Constraints

Mathematical Methods in Systems, Optimization and Control(eds. Harry Dym, Mauricio de Oliveira, Mihai Putinar). Operator Theory: Advances and Applications, Vol 222, pp. 247-258, Birkhauser, Basel, 2012.

Approximate GCDs of polynomials and sparse SOS relaxations

Joint with B. Li and L. Zhi,Theoretical Computer Science, 409(2) pp.200-210, 2008.

Semidefinite Representation of the k-Ellipse

Joint with P. Parrilo and B. Sturmfels,IMA Volume 146: Algorithms in Algebraic Geometry

(Eds. A. Dickenstein, F.-O. Schreyer, and A. Sommese), pp. 117-132, Springer, New York, 2008.

Shape optimization of transfer functions

Joint with J. Demmel,Multiscale optimization methods and applications, pp. 313--326,

Nonconvex Optim. Appl., 82, Springer, New York, 2006.