Title of Presentation: Forty Years of Corner Polyhedra

Abstract:

This talk will discuss the evolution of corner polyhedra from their beginnings in the study of Stock Cutting problems. We will discuss both their practical and theoretical aspects. We will see that corner polyhedral are by themselves the simplest integer programs and therefore might be expected to be more amenable to analysis than the more complex I.P. s of which they are always a part. This expectation is fulfilled by some theoretical insights gained from corner polyhedra. The practical linkage stems from the fact that cutting planes for corner polyhedra are cutting planes for the complex practical problems of which they are a part. No knowledge of corner polyhedra is assumed in this talk.

Bio

Ralph Gomory was born in New York, U.S.A. in 1929. He graduated from Williams College in 1950, studied at Cambridge University, and received his Ph.D. in mathematics from Princeton University in 1954. Gomory then served in the U.S.Navy (1954-57) and then was a Higgins Lecturer and Assistant Professor of Mathematics at Princeton before joining IBM’s newly formed Research Division in 1959 as a research mathematician.

In his student and graduate student years (Williams, Cambridge, Princeton), Gomory published papers on nonlinear differential equations, but his years in the Navy turned his attention to the applied mathematics of operations research. Back at Princeton he obtained the first general cutting-plane algorithms, which established the field of integer programming.

At IBM Research in the early 1960’s, Gomory published papers with Paul Gilmore on the knapsack, traveling salesman and cutting-stock problems, and with T. C. Hu on flows in multi-terminal networks and continua. In the late 1960’s, he developed the asymptotic theory of integer programming and introduced the concept of corner polyhedra. In the early 1970’s, he collaborated with Ellis Johnson in investigating subadditive functions related to corner polyhedra that could also play a role in producing cutting-planes.

Gomory became Director of Research for IBM in 1970, with line responsibility for IBM’s Research Division. During his 18 years as Director of Research the Research Division made a wide range of contributions to IBM’s products, to the computer industry, and to science. The Zurich Research Laboratory did the work that resulted in two successive Nobel Prizes in physics, Yorktown Heights Research was the birthplace of what is now known as RISC architecture, and San Jose was the birthplace of the concept, theory and first prototype of relational databases.

Gomory, who had become the IBM Senior Vice President for Science and Technology retired from IBM in 1989 and became President of the Alfred P. Sloan Foundation. During his tenure as President he led the foundation into a long list of fields relevant to major national and scientific problems. The foundation pioneered in on-line learning and organized the worldwide Census of Marine Life. In r 2007, after 18 years as President, Gomory became President Emeritus and joined New York University as a Research Professor.

Gomory is a member of the U.S. National Academy of Sciences, the U.S. National Academy of Engineering, and the American Philosophical Society. He has been awarded eight honorary degrees and many prizes including the Lanchester Prize in 1963, the Harry Goode Memorial Award of the American Federation of Information Processing Societies in 1984, the John von Neumann Theory Prize in 1984, the Medal of the Industrial Research Society in 1985, the IEEE Engineering Leadership Recognition Award in 1988, the National Medal of Science awarded by the President of the United States in 1988, the Arthur M. Bueche Award of the National Academy of Engineering in 1993, the Heinz Award for Technology, the Economy and Employment in 1998, the Madison Medal Award of Princeton University in 1999, the Sheffield Fellowship Award of the Yale University Faculty of Engineering in 2000, the International Federation of Operational Research Societies Hall of Fame in 2005, and the Harold Larnder Prize of the Canadian Operational Research Society in 2006.

In addition to his mathematical work Gomory has written on the nature of technology development, research in industry, and industrial competitiveness, and on models of international trade involving changing technologies and economies of scale. He is the author, with Professor William Baumol, of the book “Global Trade and Conflicting National Interests” MIT Press 2001.