Andrea Lodi, the Andrew H. and Ann R. Tisch Professor at Jacobs Technion—Cornell Institute at Cornell Tech and a member of the School of Operations Research and Information Engineering graduate field... Read more about ORIE’s Lodi named winner of prestigious Farkas Prize
Students, friends and colleagues join in Mike Todd’s retirement celebration
Todd has spent more than 40 years at Cornell, teaching and advancing the field of optimization.
“Your impact has been profound and long lasting,” ORIE Director David Shmoys told retiring Leon C. Welch Professor Michael J. Todd at a banquet in his honor. You have “shaped this place to be what it is today,” he said.
Todd’s retirement celebration, a “ToddFest,” included a technical symposium and banquet on campus and a barbecue party at Robert Treman State Park in Ithaca. “That all of you are attending is a tribute to Mike,” Shmoys said at the banquet. “Many of you have travelled long distances to get here,” he noted.
More than 75 people were at the celebration, and several others from all over the world who were not able to attend in person contributed video clips that were compiled into an entertaining video shown at the banquet.
Todd himself travelled a considerable distance to arrive at Cornell. He was born in Chelmsford, northeast of London, and received his BA in Mathematics from Cambridge University before coming to the U.S. for a Ph.D. in Administrative Sciences from Yale. He spent two years as a lecturer and assistant professor at the University of Ottawa before joining Cornell in 1973, and (other than during sabbaticals) has been here ever since.
Research and teaching
Robert Freund, Theresa Seley Professor in Management Science at MIT’s Sloan School of Management characterized Todd’s professional career as “Moving Optimization Forward.” Todd did so with fundamental contributions to fixed-point algorithms and interior-point methods, among the many research topics covered in at least 170 papers, individually and with more than 60 coauthors, several of whom were at the event.
- Todd contributed to the theory of fixed points and developed new methods for computing them. When the mathematical transformation of a number or other value yields the same value back again, the value is called a fixed point. Finding such fixed points turns out to be important in physics, economics (including game theory), and logic, and even underlies the computation of page rank on the World Wide Web. A key challenge of many algorithms to compute fixed points (in three dimensions) is to decompose a cube into tetrahedra in a certain constrained and efficient way – called a triangulation - and repeat the procedure at smaller and smaller scales. In an early paper, Todd developed new triangulations and devised a way to measure their efficiency in arbitrarily many dimensions. .
- Todd is also known for work on computing solutions to linear programming (LP) problems and especially for contributing to the understanding of interior-point methods. Interior-point methods solve LP problems as well as more general classes of problems by a different approach than the “classical” simplex method that is used routinely to solve a broad variety of resource allocation problems in industry and government. Geometrically, the simplex method (which Todd has analyzed probabilistically to explain its surprising practical efficiency) traverses successive corners of a polytope (a multi-dimensional polygon) until a provable solution is found. Interior-point methods proceed instead through the interior of the polytope to a solution, which can speed up the computation. With K. C. Toh Ph.D. ’96 and R. Tütüncü PhD ’96 Todd developed SDPT3, a computer code to solve the more general class of problems known as semi-definite programs (SDP). The name of the program is a combined acronym for the SDP class and the authors).
As Donald Goldfarb, Alexander and Hermine Avanessians Professor of Industrial Engineering and Operations Research at Columbia pointed out, Todd’s work has particular importance for large-scale problems arising in machine learning, video analysis, and other areas essential to today’s data-driven economy.
Todd’s student Levent Tunçel PhD ’93, a professor at the University of Waterloo, Canada, said that he was “still inspired by the lecture in his first class with Todd at Cornell, and by his latest paper – really a piece of art.” Several participants also noted Todd’s sharp questions in weekly seminar talks given by others on a wide variety of topics, many of which are unrelated to Todd’s own research. Tim Huh PhD ‘03 said that these questions inspired him to learn the entire spectrum of operations research, not just the narrow topic of his own research.
Throughout the celebration, an array of speakers commented on Todd’s qualities as a teacher and colleague. Thomas Magnanti, an MIT professor and former engineering dean who is currently president of Singapore University of Technology and Design, noted Todd’s “voracious appetite” for ideas and activities, as well as his “intellect, passion, and enthusiasm.” Goldfarb, found that enthusiasm infectious, and listed the broad range of topics it encompasses, from food to fast cars and motorcycles, from Russian drinking songs and Morris dancing to social justice. Others commented on Todd’s agility and speed in filling a whiteboard with mathematics.
Yurii Nesterov, a professor at the Center for Operations Research and Economics at the Catholic University of Louvain, Belgium, noted that it had been difficult for himself and other Russian researchers who came to the US after the cold war to establish collaborations and overcome their inexperience with “Western life,” and that Todd had helped him, Arkadi Nemirovski and the late Leonid G. Khachiyan to make the transition.
George Nemhauser, A. Russell Chandler lll Chair and Institute Professor at Georgia Institution of Technology, was Director of ORIE from 1977 to 1983. He said “the best decision I’ve made was when we hired Mike Todd at Cornell.” He characterized Todd as “the broadest guy,” and noted that the celebration also honored his wife, Marina, who was Nemhauser’s editorial assistant when he was the editor of the flagship journal Operations Research.
ORIE’s Professor James Renegar told the group that Ithaca sculptor Rob Licht has been commissioned to create a sculpture based on Todd’s triangulation work that would be presented to him once completed. The resulting sculpture represents the corners and edges of the tetrahedra in a particular triangulation that was featured in Todd’s 1975 publication, with the lower part showing a four-fold refinement of the upper.
“I am verklempt,” Todd told the guests following the series of banquet speeches. “Thank you for 41 years of wonderful inspiration. Thanks to Cornell, with its great students and wonderful colleagues, who inspired me to do the work I have done, and with its environment and opportunity to talk to colleagues in different fields.”