Journal Publications
Book Chapters

Journal Publications

  • 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 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, 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 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.
  • Book Chapters

  • 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.