Thomas F. Coleman
Professor
Director: Cornell Theory Center
Director: Center for Applied Mathematics
coleman@cs.cornell.edu
PhD Waterloo, 1979
Our research is concerned with the design and understanding of practical and efficient numerical
algorithms for continuous optimization problems. Our
primary emphasis is the development of algorithms for
large-scale optimization. In the last year we focused on
two major application areas: image segmentation and
computational finance. |
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Adrian Mariano, a Ph.D. student in the Center for Applied Mathematics, completed his Ph.D. thesis under me in May1999: `Image Processing with Total Variation Minimization'. A new optimization-based image segmentation approach was developed in this work with specific application to the
problem of identifying pulmonary nodules in X-ray computed tomography (CT) scans.
With colleagues Yuying Li and Arun Verma we have developed a new method for determining a smooth volatility surface with application to the generalized Black-Scholes model used for pricing options in mathematical finance. The crux of our approach is the formulation of a tractable
optimization problem that yields a sufficiently smooth surface consistent with known option prices. With applied mathematics student Yohan Kim we are beginning to explore further uses and general applicability of our surface reconstruction technique.
University Activities
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Director: Cornell Theory Center
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Director: Cornell Computational
Finance Institute (55 Broad
Street, New York City)
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Director: Center for Applied
Mathematics
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Member: Computing and
Information Sciences Task
Force, Cornell task Force on
Genomics, CIO Search
Committee
Professional Activities
- Chair: SIAM Activity Group on
Optimization
- Program Committee: Automatic
Differentiation 2000,
INRIA,
France
- Member: Advisory Board,
Brookhaven Center for Data
Intensive Computing
- Organizer and Instructor, SIAM
Short Course on `Optimization
in Finance', May 1999
- Editorial Board: Applied
Mathematics Letters; SIAM
Journal Scientific Computing;
Computational Optimization
and Applications, Comm. on
Applied Non-linear Analysis,
Mathematical Modeling and
Scientific Computing
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Editorial Advisory
Board: SIAM
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Referee/Reviewer:
Mathematical
Programming,
Computational Optimization
and Applications, SIAM
Journal Optimization, SIAM
Journal Scientific Computing,
Department of Energy, NSF Lectures
- An inverse problem in finance.
Sixth SIAM Conference on
Optimization, May 1999,
Atlanta
- Computing a smooth local
volatility function. Conference
on Approximation and
Complexity in Numerical
Optimization: Continuous and
Discrete Problems, Univ. of Florida, Feb. 1999
- —. Renaissance Technologies Corp.,
March 1999
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—. International Conference on
Nonlinear Programming and
Variational Inequalities, Hong Kong,
Dec. 1998
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—. Morgan Stanley, New York, Nov
1998
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—. Univ. of Toronto, Numerical
Analysis Seminar, October 1998
- —. Computational and Quantitative
Finance '98, New York, Sept. 1998
Publications
- Reconstructing the unknown local
volatility function. Journal of
Computational Finance 2, 3 (Spring
1999), 77-102 (with Y. Li and A.Verma)
- The efficient computation of structured gradients using automatic
differentiation. SIAM Journal on
Scientific Computing 20 (1999),
1430-1437 (with G. Jonsson)
- SIAM Short Course Notes on An Introduction to Optimization in
Finance (May 1999) (with R.
Dembo)
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An inverse problem in finance. SIAG/OPT Views-and-News 10, 2(May 1999), 4-8
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Optimization Toolbox, Users Guide, Version 2. (The Mathworks, Inc.),
(Jan. 1999) (with M. Branch, and A.
Grace)
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