1998 - 1999 CS Annual Report                                                                  Faculty
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Thomas F. Coleman

Director: Cornell Theory Center
Director: Center for Applied Mathematics

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 seg
mentation 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 
  • Director: Cornell Theory Center 
  • Director: Cornell Computational Finance Institute (55 Broad Street, New York City) 
  • Director: Center for Applied Mathematics 
  • 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  
  • Editorial Advisory Board: SIAM  
  • Referee/Reviewer: Mathematical Programming, Computational Optimization and Applications, SIAM Journal Optimization, SIAM Journal Scientific Computing,
    Department of Energy, NSF 
  • 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  
  • . International Conference on Nonlinear Programming and Variational Inequalities, Hong Kong, Dec. 1998  
  • . Morgan Stanley, New York, Nov 1998  
  • . Univ. of Toronto, Numerical Analysis Seminar, October 1998 
  • . Computational and Quantitative Finance '98, New York, Sept. 1998 
  • 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)  
  • An inverse problem in finance. SIAG/OPT Views-and-News 10, 2(May 1999), 4-8  
  • Optimization Toolbox, Users Guide, Version 2. (The Mathworks, Inc.), (Jan. 1999) (with M. Branch, and A. Grace)