Homepage of Jiawang Nie


Assistant Professor of Mathematics
University of California, San Diego

Address:
UCSD, Mathematics Department
9500 Gilman Drive
La Jolla, CA 92093

Eamil: njw  "AT"  math.ucsd.edu
Phone: (626)395-2245


 

Research Interests:

  •  Numerical Optimization
  •  Semidefinite Programming
  •  Computational Real Algebra
  •  Numerical Analysis
  •  Scientific Computing

    • Education

  • Ph.D.  University of California at Berkeley , 2006.
  • M.S.  Chinese  Academy of Sciences,  2000.
  • B.S.  Xi'an  Jiaotong  University,  1997.

    • Preprints and Publications

  • "Matrix cubes parametrized by eigenvalues" (with B. Sturmfels), preprint, 2008.
  • "Structured Semidefinite Representation of Some Convex Sets"(with J.W. Helton), preprint, 2008.
  • "Algebraic Degree of Polynomial Optimization"(with K. Ranestad), preprint, 2008.
  • " Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets "(with J.W. Helton), preprint, 2007.
  • " Semidefinite Representation of Convex Sets"(with J.W. Helton, revised version, April 22, 2008), preprint, 2007.
  • " Semidefinite Representation of the k-Ellipse"(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.
  • "Semidefinite Relaxation Bounds for Indefinite Homogeneous Quadratic Optimization"(with S. He, Z. Luo, and S. Zhang), to appear in SIAM Journal on Optimization.
  • "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), Proceedings of the American Mathematical Society, 136 (2008), 73-76.
  • "Sparse SOS relaxations for minimizing functions that are summations of small polynomials"(with J. Demmel), preprint, 2006.
  • "Sum of squares method for sensor network localization", to appear in Computational Optimization and Applications.
  • "Global minimization of rational functions and the nearest GCDs" (with J. Demmel and M. Gu),  Journal of Global Optimization, Vol. 40 (2008), no.4, 697-718.
  • " On the complexity of putinar's positivstellensatz" (with M. Schweighofer),  Journal of Complexity 23(2007), pp.135-150.
  • " Representations of positive polynomials on non-compact semialgebraic sets via KKT ideals" (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"(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" (with J. Demmel).Journal of Global Optimization Vol. 33(2005), pp. 511-525.
  • "Shape optimization of transfer functions", (with J. Demmel), Multiscale optimization methods and applications , pp. 313--326, Nonconvex Optim. Appl., 82, Springer, New York, 2006.

    • Teaching

  • Math 54  Summer  2004

    • Conferences, Seminars and Workshops

  • Southern California Algebra and Optimization Day: March 6 2008.

  • SIAM Conference on Optimization: May 10-13, 2008.