Algorithms, Applied Probability, Optimization

Office: 229 Rhodes

Phone: 607.255.9135

Website: click here

Fax: 607.255.9129

Michael Todd is the Leon C. Welch Professor of Operations Research and Industrial Engineering. He received his B.A. in Mathematics from Cambridge University, England in 1968 and his Ph.D. in Administrative Sciences from Yale University in 1972. Todd joined the School of Operations Research and Industrial Engineering in 1973.

Todd is interested in polynomial-time algorithms for linear and semidefinite programming. Together with two former graduate students, he has developed the software package SDPT3 for such problems. He has also worked on probabilistic analysis of the simplex method, the ellipsoid method, and simplicial algorithms for fixed-point problems and computing economic equilibria, and is currently working with a student on first-order methods for nonsmooth optimization.

In general, Todd’s research deals with interior-point methods for linear and convex programming, and with the barrier functions that make these algorithms efficient. Problems such as semidefinite programming and second-order cone programming have rich applications in fields as diverse as structural optimization, control theory, optimal design in statistics, and combinatorial optimization. They also have a powerful duality theory and efficient algorithms for their solution.

Select Publications

“Solving semidefinite-quadratic linear programs using SDPT3”. Mathematical Programming 95: 189 - 217 (2003). (With R. H. Tutuncu and K.C. Toh)

“The many facets of linear programming”. Mathematical Programming 91: 417- 436 (2002).

“Semidefinite optimization”. Acta Numerica 10: 515 - 560 (2001).

“Self-scaled barriers and interior-point methods for convex programming”. Mathematics of Operations Research 22: 1 - 42 (1997). (With Y.E. Nesterov)

“Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems”. Mathematical Programming 35:173 - 192 (1986).

Lectures

Conic programming. Summer School lecture at ICCOPT I, Troy, August 2004.

Conic linear optimization. Main speaker, Second Latin American Congress of Mathematicians, Cancun, June 2004.

Detecting infeasibility in infeasible-interior-point methods for optimization. Plenary lecture at the Foundations of Computational Mathematics Conference, Minneapolis, August 2002.

The many facets of linear programming. Plenary lecture at the 18th International Symposium on Mathematical Programming, Atlanta, August 2000.

Professional Activities

Institute for Operations Research and the Management Sciences

Mathematical Programming Society

Society for the Foundations of Computational Mathematics

Society for Industrial and Applied Mathematics

University Activities

Director, School of Operations Research and Industrial Engineering, 1985 -1986

Director, Center for Applied Mathematics, 1986 - 1989

Awards and Honors

Guggenheim Fellow, 1980

Sloan Foundation Fellow, 1981

George B. Dantzig Prize, SIAM and the Mathematical Programming Society, 1988

John von Neuman Theory Prize, INFORMS, 2003

Fellow, INFORMS, 2004