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 focus has been on the development of algorithms for largescale optimization. A
new application area of interest is financial optimization. 

Graduate student A. Verma completed his PhD
dissertation this year. This work explored the effective use of automatic differentiation
technology in the context of largescale optimization applications. Application areas
range from inverse problems in wave propagation to the computation of volatility in
finance. Graduate student A. Florence is further exploring the use of automatic
differentiation in bifurcation problems arising in the modeling of thin shell structures.
This work is in collaboration with Prof. T. Healey (TAM).
Image segmentation and enhancement problems
frequently arise in radiology settings. Applied Math student A. Mariano, colleague Y. Li,
and I have been developing new optimizationbased algorithms for such problems. This work
is in collaboration with radiology departments at Cornell Medical School and the Univ. of
Rochester.
Many problems in mathematical finance can be
usefully posed as optimization problems. Applied Math student Y. Kim, research associates
Y. Li and J. Pusztaszeri, A. Verma, and I are studying and developing a number of such
cases. For example, we are investigating new ways to compute the famous "volatility
smile" using optimization, spline approximations, and automatic differentiation.
University Activities
Director: Cornell Theory Center
Director: Center for Applied Mathematics
Cornell CIO search committee
Professional Activities
Chair: SIAM Activity group on optimization
CoOrganizer: IMA Workshop
Editorial Board: Applied Mathematics Letters;
SIAM J. Scientific Computing; Computational Optimization and Applications; Comm.
on Applied Nonlinear Analysis, Mathematical Modeling and Scientific
Computing
Editorial Advisory Board: SIAM
Referee/Reviewer: Mathematical Programming,
Computational Optimization and Applications, SIAM J. Optimization, SIAM
J. Scientific Computing, Department of Energy, NSF
Lectures
Automatic differentiation and structure. IMA
Workshop on TemplateDriven Automatic Differentiation for LargeScale Scientific and
Engineering Applications. Univ. Minnesota, Minneapolis, June 29  July 3, 1997.
When automatic differentiation is not automatic.
AFOSR Workshop on Optimal Design and Control, Oct. 2, 1997, Washington D.C.
Financial optimization in MATLAB. Algorithmics
Risklab Inaugural Meeting, Toronto, Ontario, Canada, Oct. 16, 1997.
Structured automatic differentiation. Operations
Research, Cornell, Dec. 1997.
Publications
Structure and efficient Hessian calculation. Advances
in Nonlinear programming, Proc. 1996 Int. Conf. Nonlinear Programming, Y. Yuan ed.,
Kluwer Academic Publishers, (1998), 5772.
The efficient computation of sparse Jacobian
matrices using automatic differentiation. SIAM J. Scientific Computing 19 (1998),
12101233 (with A. Verma).
Combining trust region and affine scaling for
linearly constrained nonconvex minimization. Advances in Nonlinear Programming, Y.
Yuan, ed., Kluwer Academic Publishers (1998), 219250 (with Y. Li).
Largescale optimization with applications. IIII.
The IMA Volumes in Mathematics and its Applications, Vol. 9294, SpringerVerlag.
(1997) (with L. Biegler, A. Cown, F. Santosa).
