Stephen A. Vavasis

Favorite links

U. Waterloo

Workshops and conferences

SIAM Annual Meeting, July 12-16, 2010, Pittsburgh, Pennsylvania featuring minisymposia on First Derivative Methods for Convex Optimization and on Matrix Rank Minimization.
SIAM Conference on Optimization, May 16-19, 2011, Darmstadt, Germany.
Housholder Symposium XVIII, June 12-17, 2011, Tahoe City, California.
Fields workshop on optimization, Sept. 26-29, 2011, Toronto, ON.
SIAM Conference on Algebraic Geometry, Oct 6-9, 2011, Raleigh, North Carolina.
Fields workshop on symbolic-numeric computation, November 16-19, 2011, Waterloo, ON.
International Symposium on Mathematical Programming, 2012 August 19-24, Berlin, featuring two invited minisymposia (see here and here) on first-derivative and interior methods in convex optimization.
Workshop on Large-Scale Conic Optimization, 2012 November 19-23, Institute for Mathematical Sciences, National University of Singapore.
Sparse Representations of Functions: Analytic and Computational aspects, 2012 December 10-14, DFG Research Centre Matheon, Technical University of Berlin.

Professional societies:

SIAM
Mathematical Optimization Society (Formerly Math Programming Society)

Research supported by:

Professor & University Research Chair (PhD, Stanford, 1989)
Department of Combinatorics & Optimization
MC 6054 (Temporarily relocated to MC 4008 effective 2013-01-30)
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 Fall 2011 I taught CO 463/663: Convex Analysis and Optimization
In Fall 2012 I am teaching CO602/CM740, Fundamentals of Optimization.

I also taught a course on compressive sensing in W'09 and wrote some lecture notes and exercises on compressive sensing.

Research and Publications

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

Complexity issues in continuous optimization,
Convex optimization and its application to data mining,
Efficient algorithms for optimization, and
Linear algebra problems arising in optimization.

I have also in the past been interested in geometric problems arising in scientific computing and numerical linear algebra arising in differential equations.

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) Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes, BIT Numerical Mathematics, Volume 50 (2010), Issue 4, 863-884.
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). Final version appeared in Engineering with COmputers, posted on line 2011-June-11, print edition to appear.
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; published paper.)
B. Ames and S. Vavasis, Convex relaxation for the planted k-disjoint-clique problem (arxiv link)
X. V. Doan and S. Vavasis, Finding approximately rank-one submatrices with the nuclear norm and l₁ norm (arxiv link). Unpublished proof of NP-hardness of LAROS problem.
X. V. Doan, K.-C. Toh and S. Vavasis, A proximal point algorithm for sequential feature extraction applications (arxiv link)
S. Karimi and S. Vavasis, Conjugate gradient with subspace optimization (arxiv link).
N. Gillis and S. Vavasis, Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization (arxiv link).
S. Sastry, S. Shontz, and S. Vavasis, A log-barrier method for mesh quality improvement and untangling, Final version appeared in Engineering with Computers, Nov 2012 (Springer Link web publication). Preliminary version appeared in Proceedings of the 2011 International Meshing Roundtable.

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.