## Emeritus Faculty Profile

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## Michael Jeremy Todd

### Biography

Michael Todd received his B.A. from Cambridge University, UK, in 1968, and his Ph.D. from Yale University, New Haven, Connecticut, in 1972. He joined Cornell University in 1973, where he is currently the Leon C. Welch Professor of Operations Research and Information Engineering. The focus of his research has been on the development and analysis of algorithms for continuous optimization problems, including simplicial algorithms for fixed-point problems, simplex and ellipsoid algorithms for linear programming, interior-point methods for semidefinite and cone programming, and first-order methods for ellipsoid optimization problems.

### Research Interests

In general, Professor Todd is concerned with algorithms for certain classes of convex programming problems and their computational complexity. Examples include pivoting algorithms for quadratic programming and linear complementarity problems, the ellipsoid algorithm for linear and convex programming, interior-point methods for linear and semidefinite and more general conic programming problems, and first-order methods for certain ellipsoid optimization problems. He has also, with two former graduate students, produced the widely-used SDPT3 software package for linear, second-order, and semidefinite programming problems. Work continues on ellipsoid optimization problems, on questions in robust optimization, and on trying to understand the excellent real-world performance of interior-point methods.

### Teaching Interests

Professor Todd used both Videonote and lecture notes posted on the course home page for ORIE 3300/5300, despite some concerns with losing attendance. Students really appreciated being able to catch up on missed lectures due to job interviews, etc., and attendance suffered only slightly. Lectures covered the theory of linear programming and algorithms for solving these problems, while most of the recitations provided hands-on experience with using the algebraic modeling language AMPL to represent real-life problems; AMPL models were also covered in the lectures, to stress the importance of modeling. Problem sets and exams dealt with both aspects of the course. ORIE 6310 dealt with extensions of linear programming, with a focus on complexity issues, including instances requiring exponential time for pivoting algorithms, expected polynomial-time pivoting algorithms, the diameter of polyhedra, and the informational complexity of nonlinear programming.

### Service Interests

Michael Todd is currently the chair of the SIAM Activity Group on optimization, as well as the managing editor for the journal Foundations of Computational Mathematics. He was previously the editor-in-chief of Mathematical Programming and the chair of the Society for the Foundations of Computational Mathematics, and has served on the editorial boards of several journals and book series.

### Selected Publications

- 2008. "Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids." Optimization Methods & Software 23 (1): 5-19. .
- 2003. "Solving semidefinite-quadratic-linear programs using SDPT3." Mathematical Programming 95 (2): 189-217. .
- 2001. "Semidefinite Optimization." Acta Numerica 10: 515-560. .
- 1997. "Self-scaled barriers and interior-point methods for convex programming." Mathematics of Operations Research 22 (1): 1-42. .
- 1986. "Polynomial Expected Behavior of a Pivoting Algorithm for Linear Complementarity and Linear-Programming Problems." Mathematical Programming 35 (2): 173-192. .

### Selected Awards and Honors

- George B. Dantzig Prize (Mathematical Programming Society (MPS) and SIAM) 1988
- John von Neumann Theory Prize (INFORMS) 2003
- Fellow (Institute for Operations Research and the Management Sciences (INFORMS)) 2004
- Fellow (Society of Industrial and Applied Mathematics (SIAM)) 2009
- College of Engineering Excellence in Teaching Award (Cornell University) 2009

### Websites

### Education

- BA (MATHEMATICS), CAMBRIDGE UNIV (UK), 1968
- Ph D (ADMINISTRATIVE SCIENCES), YALE UNIVERSITY, 1972