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 large-scale 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 large-scale 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 optimization-based 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

• Co-Organizer: IMA Workshop

• Editorial Board: Applied Mathematics Letters; SIAM J. Scientific Computing; Computational Optimization and Applications; Comm. on Applied Non-linear 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 Template-Driven Automatic Differentiation for Large-Scale 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), 57-72.

• The efficient computation of sparse Jacobian matrices using automatic differentiation. SIAM J. Scientific Computing 19 (1998), 1210-1233 (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), 219-250 (with Y. Li).

• Large-scale optimization with applications. I-III. The IMA Volumes in Mathematics and its Applications, Vol. 92-94, Springer-Verlag. (1997) (with L. Biegler, A. Cown, F. Santosa).