Jiawang Nie

Curriculum Vitae

Research Fellow at IMA
University of Minnesota

400 Lind Hall, IMA
University of Minnesota
207 Church St. SE
Minneapolis, MN 55455

Eamil: njw  "AT"  ima.umn.edu
Phone: (612) 626-0788

Research Interests:

  •  Numerical Optimization
  •  Real Algebraic Geometry
  •  Computational Algebra
  •  Operations Research
  •  Sensor Network Localization
  • My Education

    Papers and Preprints

  • " Semidefinite Representation of Convex Sets"(with J.W. Helton), preprint, 2007.
  • " Semidefinite Representation of the k-Ellipse"(with P. Parrilo and B. Sturmfels), preprint, 2007.
  • "Semidefnite Relaxation Bounds for Indefinite Homogeneous Quadratic Optimization"(with S. He, Z. Luo, and S. Zhang), preprint, 2006.
  • "The Algebraic Degree of Semidefinite Programming"(with K. Ranestad and B. Sturmfels), preprint, 2006.
  • "An elementary and constructive proof of Hilbert's 17th Problem for matrices"(with C.Hillar), preprint, 2006.
  • "Sparse SOS relaxations for minimizing functions that are summation of small polynomials"(with J. Demmel), preprint, 2006.
  • "Sum of squares method for sensor network localization", preprint, 2006.
  • "Global minimization of rational functions and the nearest GCDs" (with J. Demmel and M. Gu),  to appear in Journal of Global Optimization.
  • " On the complexity of putinar's positivstellensatz" (with Markus Schweighofer),  Journal of Complexity 23(2007) 135-150.
  • " Representations of positive polynomials on non-compact semialgebraic sets via KKT ideals" (with James W. Demmel and  Victoria 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"(with James W. Demmel and Bernd Sturmfels), Mathematical Programming, Series A, Vol. 106 (2006), No. 3, 587-606.
  • "Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares" (with James W. Demmel).Journal of Global Optimization Vol. 33(2005), p. 511-525.
  • "Shape optimization of transfer functions", (with James W. Demmel), multiscale optimization methods and applications , eds. W. Hager, P. Pardalos, S. Huang, et al., pp. 313-326, Springer series on nonconvex optimization and its application series, 2005.
  • "A predictor-corrector algorithm for  QSDP combining Dikin-type and newton centering steps"(with Y. Yuan),  Annals of Operations Research, 103(2001) 115-133.
  • " A potential reduction algorithm for a new SDP problem"(with Y. Yuan),  Science in China,  Vol.43, No.1, Jan.  2000.
  • Awards

    My Teaching

    Softwares for Polynomial Optimization

  • GloptiPoly
  • SparsePOP