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
Numerical Optimization Semidefinite Programming Computational Real Algebra Numerical Analysis Scientific Computing
Ph.D. University of California at Berkeley , 2006. M.S. Chinese Academy of Sciences, 2000. B.S. Xi'an Jiaotong University, 1997.
"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.
Math 54 Summer 2004
Southern California Algebra and Optimization Day: March 6 2008.
SIAM Conference on Optimization: May 10-13, 2008.