Stephen A. Vavasis

Favorite links

U. Waterloo

Main page
WatIAM (search for a UW person)
Math Faculty
C & O Dept
Computational Mathematics including new Masters program
Google search of Waterloo

Workshops and conferences

ICCOPT, August 13-16, 2007, McMaster University, Hamilton, ON.
SIAM Conference on Geometric Design and Computing, November 4-8, 2007, San Antonio, TX, featuring a minisymposium on numerical methods for intersection problems
Waterloo Symposium on Numerical Analysis (in commemoration of Gene Golub), February 29, 2008, Waterloo.
SIAM Optimization Meeting, May 10-13, 2008, Boston, MA featuring a minisymposium on nonnegative matrix factorization.
Householder Symposium XVII on numerical linear algebra, June 1-6, 2008, Zeuthen, Germany.
Modeling and Optimization: Theory and Applications 2008 (MOPTA), August 18-20, 2008, University of Guelph, Ontario.
International Symposium on Mathematical Programming, August 24-28, 2009, Chicago, Illinois.
SIAM Conference on Applied Linear Algebra, October 26-29, 2009, Monterey Bay, California featuring a minisymposium on recent progress in rank minimization.
Workshop on Sparse Random Structures: Analysis and Computation (10w5033), Banff International Research Station, Alberta, Canada, January 24-29, 2010.

Professional societies:

Research supported by:

Professor & University Research Chair (PhD, Stanford, 1989)
Department of Combinatorics & Optimization
MC 6054
University of Waterloo
200 University Avenue W.
Waterloo, ON N2L 3G1
Canada

email: vavasis@math.uwaterloo.ca
phone: +1-519-888-4567 ext. 32130
fax: +1-519-725-5441

Courses

In Winter 2009 I taught CO 769: Topics in Continuous Optimization. The topic this term is compressive sensing and related areas.
In Fall 2009 I am teaching CO 602: Fundamentals of Optimization

Research and Publications

My research interests are continuous optimization and numerical analysis. More specifically, I am interested in:

Complexity issues in continuous optimization
Numerical methods for boundary value problems
Geometric problems arising in scientific computing
Numerical linear algebra arising in differential equations and optimization

I have a few recent manuscripts available on-line:

S. Vavasis and Y. Ye, ``A primal dual accelerated interior point method whose running time depends only on A'' (compressed postscript, 170k). Final version appeared in Math. Progr. 74 (1996) 79-120.
P. Hough and S. Vavasis, ``Complete orthogonal decomposition for weighted least squares'' (gzip'd postscript, 84k; plain postscript, 330k). Final version appeared in SIAM J. Matrix Anal. Appl., 18 (1997) 369-392.
S. Mitchell and S. Vavasis, ``An aspect ratio bound for triangulating a d-grid cut by a hyperplane'' (compressed postscript, 118k; plain postscript, 339k). Extended abstract appeared in Proc. 1996 Symp. Comput. Geom., ACM Press, 48-57.
T. Driscoll and S. Vavasis, ``Numerical conformal mapping using cross-ratios and Delaunay triangulation'' (gzip'd postscript, 139k; plain postscript, 395k). Final version appeared in SIAM J. Sci. Comp. 19 (1998) 1783-1803.
S. Mitchell and S. Vavasis, ``Quality Mesh Generation in Higher Dimensions'' (gzip'd postscript, 130k; plain postscript, 388k). Final version appeared in SIAM J. Comput. 29 (2000) 1334-1370.
E. Bobrovnikova and S. Vavasis, ``Accurate Solution of Weighted Least Squares by Iterative Methods'' (gzip'd postscript, 105k; plain postscript, 349k). Final version appeared SIAM J. Matrix An. App 22 (2001) 1153-1174.
E. Bobrovnikova and S. Vavasis, ``A Norm Bound for Projections with Complex Weights'' (gzip'd postscript, 106k; plain postscript, 215k). Final version appeared Linear Alg. Appl. 307 (2000) 69-75.
V. Howle and S. Vavasis, ``Preconditioning complex-symmetric layered systems arising in electric power modeling'' (gzip'd postscript, 42k; plain postscript, 156k).
S. Vavasis, ``A note on efficient computation of the gradient in semidefinite programming'' (gzip'd postscript, 99k; plain postscript, 196k).
G. Jónsson and S. Vavasis, ``Solving polynomials with small leading coefficients'' (gzip'd postscript, 100k; plain postscript, 290k). Final version appeared: SIAM J. Matrix Analysis App., 26 (2005) 400-414.
V. Howle and S. Vavasis, ``An iterative method for solving complex-symmetric systems arising in electric power modeling'' (gzip'd postscript, 123k; plain postscript, 343k). Final version appeared: SIAM J. Matrix Analysis App., 26 (2005) 1150-1178
G. Jónsson and S. Vavasis, ``Accurate solution of polynomial equations using Macaulay resultant matrices'' (gzip'd postscript, 284k; plain postscript, 689k). Final version appeared: Mathematics of Computation, 74 (2005) 221-262
S. Vavasis, ``A Bernstein-Bezier sufficient condition for invertibility of polynomial mapping functions'' (revised 3 Nov 2001) (gzip'd postscript, 100k; plain postscript, 200k).
K. Papoulia and S. Vavasis, ``Time continuity in cohesive finite element modeling'' (pdf, 319k). Final version appeared: International Journal for Numerical Methods in Engineering 58(5) 679-701, 2003.
P. Ganguly, S. Vavasis and K. Papoulia, ``An algorithm for two-dimensional mesh generation based on the pinwheel tiling'' (pdf, 289k) SIAM J. Scientific Comput., 28 (2006) 1533-1562.
E. Boman, B. Hendrickson, and S. Vavasis, ``Solving Elliptic Finite Element Systems in Near-Linear Time with Support Preconditioners'' (Arxiv link), SIAM J. Numer. Anal. 46 (2008) 3264-3284.
K. Papoulia, S. Vavasis and P. Ganguly, Spatial convergence of crack nucleation using a cohesive finite element model on a pinwheel-based mesh, International J. Numer. Meth. Eng. (pdf, 291k), 67(2006) 1-16.
Chin-Hang Sam, K. Papoulia, Stephen Vavasis, Obtaining initially rigid cohesive finite element models that are temporally convergent, Engineering Fracture Mechanics, 72 (2005) 2247-2267. (pdf, 310k)
S. Shontz and S. Vavasis, ``A linear weighted laplacian smoothing framework for warping tetrahedral meshes'' (arxiv link)
Gun Srijuntongsiri and S. Vavasis, A Fully Sparse Implementation of a Primal-Dual Interior-Point Potential Reduction Method for Semidefinite Programming, submitted to SIAM Journal on Optimization (arxiv link)
S. Vavasis, A conjecture that the roots of a univariate polynomial lie in a union of annuli (arxiv link)
Gun Srijuntongsiri and S. Vavasis, A condition number analysis of a line-surface intersection algorithm (arxiv link). SIAM J. Sci. Comput 30 (2008) 1064-1081.
S. Shontz and S. Vavasis, ``A robust solution procedure for hyperelastic solids with large boundary deformation'' (arxiv link)
Gun Srijuntongsiri and S. Vavasis, Properties of polynomial bases used in line-surface intersection algorithm, (arxiv link)
S. Vavasis, On the complexity of nonnegative matrix factorization, (arxiv link). Final version appeared, SIAM J. Optim. Volume 20, Issue 3, pp. 1364-1377 (2009).
Gun Srijuntongsiri and S. Vavasis, A condition number analysis of a surface-surface intersection algorithm (arxiv link)
M. Biggs, A. Ghodsi and S. Vavasis, Nonnegative matrix factorization via rank-one downdate, preliminary journal version from arxiv.org, ICML 2008 conference version.
B. Ames and S. Vavasis, Nuclear norm minimization for the planted clique and biclique problems, (arxiv link)

The QMG package

I have written a software package called QMG for mesh generation for the finite element method in three dimensions. QMG is available on an open-source basis by anonymous ftp. With QMG you can construct 3D geometric objects with very complicated topology (holes, internal boundaries, etc.) and automatically create an unstructured tetrahedral mesh for them. (The mesh generator is based on algorithmic work by Scott Mitchell and me.) You can also solve an elliptic boundary value problem (div (c*grad u)=f) on your domain. The package is written in C++ and Matlab and is distributed for free at the source-code level (anonymous ftp distribution began 5/5/95). It runs under Matlab and Tcl/Tk.

QMG 2.0 was released on 3 September 1999. The principal new feature in QMG 2.0 (compared to QMG 1.1) is its ability to handle curved boundaries.

Please see the on-line documentation.