Thomas F. Coleman
Director, Advanced Computing Research Institute (ACRI)
Ph.D. University of Waterloo, 1979
Our research is concerned with the design and understanding of
practical and efficient numerical algorithms for continuous
optimization problems. Our primary focus has been on the development
of algorithms for large-scale optimization: exploitation of scarcity
and use of parallelism have been two dominant themes.
Many large-scale optimization problems display scarcity in both second
derivative (Hessian) matrices and constraint matrices. We are
developing techniques and tools for the efficient calculation of
derivative matrices - often the most time-consuming, error-prone task
- using the judicious application of methods from the blossoming
subfield of automatic differentiation. Moreover, we are investigating
how to extend our approach from explicit sparse problems to dense but
structured problems. This work is joint with CS Ph.D. student Arun
Verma. Structured iterative solution techniques are being developed by
visiting Ph.D. student Shahadat Hossain.
A rich source of large-scale structured optimization problems are the
related computational areas of discrete optimal control, dynamical
systems, and boundary value problems involving systems of ordinary
differ-ential equations (and differential-algebraic equations). A
common thread in these important areas is that determination of the
relevant derivative matrices is enormously expensive. However, it
appears that structured application of automatic differentiation
techniques can dramatically lower this cost. We are investigating this
possibility with Applied Math Ph.D. student Gudbjorn Jonsson.
Various inverse problems, and image-en-hancement problems in
particular, can be posed as continuous optimization problems. A
popular approach has been to do exactly this using very smooth
(least-squares) objective functions. However, we have discovered that
significantly better "enhanced'' solutions can often be achieved using
piecewise differentiable objective functions and simple
constraints. We are developing new algorithms, including parallel
approaches, for these problems. Applications range from clearing up
noisy blurred photographs to medical ultrasonic imaging. Involved in
this work are ACRI researchers Yuying Li and Chunguang Sun and Applied
Math Ph.D. student Adrian Mariano.
- Director, Advanced Computing Research Institute
- Editorial Board: Applied Mathematics Letters; SIAM Journal on
Scientific Computing; Computational Optimization and Applications;
Communications on Applied Nonlinear Analysis, Mathematical Modeling
and Scientific Computing
- Editorial Advisory Board: SIAM
- Referee/Reviewer: Mathematical Programming; Computational Optimization
and Applications; SIAM Journal on Optimization; SIAM Journal on
Scientific Computing; Department of Energy, NSF
- Co-Organizer: Institute for Mathematics and Its Applications Workshop
Large-Scale Optimization, July 10-28, 1995, University of Minnesota
- LSOT: A large-scale optimization toolbox in Matlab. Invited
Lecture. INFORMS, Washington D.C., May 8, 1996.
- Structure and efficient Jacobian calculation. Numerical Analysis
Colloquium, University of Minnesota, April 1, 1996.
- ____. Invited Lecture. 2nd SIAM Conference on Computational
Differentiation, Santa Fe, February, 1996.
- Parallel continuation-based global optimization for molecular
conformation and protein folding. Journal of Global Optimization 8
(1996), 49-65 (with Zhijun Wu).
- An interior trust region approach for nonlinear minimization subject
to bounds. SIAM Journal on Optimization 6 (1996), 418-445 (with
- Parallel structural optimization applied to bone remodeling on
distributed memory machines. Computational Optimization and
Applications 4 (1995), 375-392 (with Shirish Chinchalkar).
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Last modified: 1 November 1996 by Denise Moore